C h a p t e r 1 T I - N s p i r e TM Te c h n o l o g y C o r n e r s
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Appendix B
TI-NspireTM Technology Corners
Texas Instruments released the new TI-Nspire CX in March
2011. The new handheld no longer has an interchangeable TI-84
­faceplate; however, the body of the Nspire CX is much slimmer
and its display is in full color. When you click ctrl menu and arrow down to Color, there are several options available: Line Color,
Fill Color, and Text Color. If you choose the Fill Color option, a
color palette will appear. Then you can select the colors you want
for your graphs. This feature is quite useful when displaying multiple graphs. When creating a bar graph, the CX even allows you to
change the color of each bar!
The keystrokes used for the new CX are the same as for the TINspire Touchpad. The keystrokes for the older Nspire “clickpad”
are still different in some ways; therefore they are still shown in
parentheses when needed.
Start by updating your device’s OS to ensure that your handheld has full capabilities. Go to education.ti.com and search under
Downloads S Software, Apps, Operating Systems… to download
the latest version of the OS. If you have the TI-Nspire computer
link software, you should be asked automatically to update your
handheld’s OS.
TOUCHPAD
CX
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Chapter 1 TI-Nspire Technology Corners
2. Histograms on the calculator
1. Insert a New Document by pressing ctrl N .
2. Insert a Lists & Spreadsheet page by arrowing down to Add Lists
& Spreadsheet.
• Name column A foreignbrn.
• Type the data for the percent of state residents born outside the
United States into the list. The data can be found on page 33.
3. Insert a Data & Statistics page: press ctrl I , arrow to Add
Data & Statistics, and press enter .
• Press tab and Click to Add Variable on the horizontal axis
will show the variables available. Select foreignbrn.
• The data should now move into a dotplot. Notice the organization of the graph. Even though the data look “lopsided” in
some places, you should consider the dots as being directly
above each other in each column.
4. To make a better graphical display, let’s move the data into a
histogram. Use the Navpad to position the pointer in an empty
space within the graph. Press ctrl menu and select Histogram.
You will now see the data move into a histogram.
You can now position the pointer ( ) over each bar to examine
the classes. The pointer will become an open hand
and the
class size will be displayed along with the number of data values
in the class.
5. Adjust the classes to match those in Figure 1.16 (page 34).
• Arrow into an empty space inside the histogram.
• Press ctrl menu and select Bin Settings, Equal Bin Width.
Enter the values shown. tab to OK and press enter . The
new histogram should be displayed.
Notice how the first bar is “off the page.” To adjust this, arrow
over until the becomes .
• Press and hold
until becomes
.
• Use the Navpad and, with the down arrow, “pull” the vertical
axis down. Keep arrowing down until the top of the tallest
histogram class is visible.
6. See if you can match the histogram in Figure 1.17 (page 35).
3. Making calculator boxplots
One of the added benefits of the TI-Nspire is its ability to plot
more than three boxplots at a time in the viewing window. Let’s
use the calculator to make parallel boxplots of the travel data for
the samples from North Carolina and New York.
1. Insert a Lists & Spreadsheet page: press ctrl I , arrow to Add
Lists & Spreadsheet, and press enter .
• Name column A ncarolina and column B newyork.
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• Enter the travel time data from page 52.
2. Insert a Data & Statistics page: press ctrl I , arrow to Add
Data & Statistics, and press enter .
• Press tab and Click to Add Variable on the horizontal axis
will show the variables available. Select ncarolina.
• The data will move into a dotplot. Use the Navpad to position
the pointer in an empty space within the graph. Press ctrl
menu and select Box Plot. You will now see the data move
into a boxplot.
• Using the Navpad, arrow over the plot. You will see the values
in the five-number summary display one by one as you move
across the boxplot.
3. To add the boxplot of newyork travel times, arrow over “ncarolina” on the horizontal axis, press ctrl menu , and choose Add X
Variable. Select newyork and the second boxplot will be added
to the page.
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• Press menu S Statistics S Stat Calculations S OneVariable Statistics. A dialogue box should appear asking for
the number of lists. Press the up arrow ( ) to 2 or type “2.”
tab to OK and press enter .
• Another dialogue box should appear. Select the lists in the
drop-down boxes: X1 list: ncarolina and X2 list: newyork.
tab between the entry boxes to enter the next list and the
column where you want the one-variable stats listed: type “c”,
tab to OK , and press enter . The numerical summaries for
both states should now be displayed.
2. You can resize the columns to see which column contains values for which state: D has summary statistics for ncarolina, and
E has summary statistics for newyork.
• Use the Navpad to place the arrow between the columns. Press
and hold
until
appears. Use the arrow keys to increase
the column width. Press
again to release the column.
4. Computing numerical summaries with technology
Let’s find numerical summaries for the travel times of North Carolina and New York workers from the previous Technology Corner.
If you haven’t already done so, enter the North Carolina and New
York data.
I , arrow to
• Insert a Lists & Spreadsheet page: press ctrl
Add Lists & Spreadsheet, and press enter . Name column A
ncarolina and column B newyork.
• Arrow down to the first empty cell in column A and type in
the data. Repeat the process for newyork in column B.
1. The Nspire can calculate one-variable statistics for several lists at
the same time (unlike the TI-84 or TI-89).
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• Repeat the same process to resize the column with one-variable statistics for newyork.
Chapter 2 TI-Nspire Technology Corners
5. From z-scores to areas, and vice versa
Finding areas: The normcdf command on the Nspire can be used to
find areas under the Normal curve. The syntax is normalcdf (lower
bound, upper bound, mean, standard deviation). Let’s use this command to confirm our answers to the examples on pages 116–118.
1. On the Home screen, select the Calculate scratchpad. This will
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take you to a calculator page that is “outside” your current document. Therefore, you do not have to worry about losing/saving
a document you are working on or about adding an unneeded
page to that document.
value corresponding to a given percentile in a Normal distribution.
For this command, the syntax is inv Norm(area to the left, m, s).
3. Let’s start with a “clean slate” by clearing the entries on our
page. To do this, press menu S Actions S Clear History.
Your scratchpad should now be blank.
What is the 90th percentile of the standard Normal distribution?
• Press menu S Statistics S Distributions S Inverse Normal.
A dialogue box will appear. Type the numbers in the dialogue
box as shown. To enter the numbers, tab between the entry
boxes. When the last number is entered, tab to OK and press
enter .
What proportion of observations from the standard Normal
­distribution are greater than –1.78?
Recall that the standard Normal distribution has mean 0 and
standard deviation 1.
2. On the Calculate scratchpad, press menu S Statistics S
­Distributions S Normal Cdf. In the dialogue box that appears,
type the numbers shown. To move between the drop-down boxes, press tab after typing each number. When the last number
is entered, tab to OK and press enter .
The proportion should now be displayed on the main screen.
Note: We chose 10,000 as the upper bound because it is many
standard deviations above the mean. These results agree with our
previous answer using Table A: 0.9625.
What proportion of observations from the ­standard Normal
distribution are between –1.25 and 0.81?
These results match our previous answer using Table A.
6. Normal probability plots
We will use the state unemployment rates data from page 122 to
demonstrate how to make a Normal probability plot for a set of
quantitative data.
1. Insert a New Document by pressing ctrl N .
2. Insert a Lists & Spreadsheet page by arrowing down to Add Lists
& Spreadsheet.
• Name column A unemploy.
• Arrow down to the first cell and type in the 50 data values.
3. Insert a Data & Statistics page by pressing ctrl I and use the
Navpad to arrow to Add Data & Statistics. Press enter .
4. Press tab to select the “Click to add variable” for the horizontal
axis. Arrow to unemploy and press enter to select it. The data
will now move into a dotplot.
5. Arrow up into an empty region of the dotplot and press ctrl
.
menu . Select Normal Probability Plot and press
The following screen shot confirms our earlier result of 0.6854
using Table A.
Interpretation: The Normal probability plot is quite linear, so it is
reasonable to believe that the data follow a Normal distribution.
Working backward: The Nspire invNorm function calculates the
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Chapter 3 TI-Nspire Technology Corners
7. Scatterplots on the calculator
1. Insert a New Document by pressing ctrl N .
2. Insert a Lists & Spreadsheet page by arrowing down to Add Lists
& Spreadsheet.
• Name column A points and column B wins.
• Type the corresponding values into each column. The data
list follows.
Points:
34.8
36.8
25.7
25.5
32.0
15.8
Wins:
12
11
8
7
10
5
Points:
35.7
16.1
25.3
30.1
20.3
26.7
Wins:
13
2
7
11
5
6
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Miles
driven
70,583 129,484 29,932 29,953 24,495
75,678
Price
(in dollars)
21,994
9500
28,986 31,891 37,991
Miles
driven
34,077
58,023
44,447 68,474 144,162 140,776 29,397 131,385
Price
(in ­dollars)
34,995
29,988
22,896 33,961 16,883
29,875 41,995 41,995
8359
4447
20,897 27,495 13,997
1. Insert a New Document by pressing ctrl N .
2. Insert a Lists & Spreadsheet page by arrowing down to Add Lists
& Spreadsheet.
• Name column A miles and column B price.
• Type the corresponding values into each column.
3. Graph the data in a scatterplot putting miles on the horizontal axis and price on the vertical axis. Refer to the previous
TI-Nspire Technology Corner.
4. To add a least-squares regression line, first ctrl
back to the
Lists & Spreadsheet page.
5. Press menu , and arrow to Statistics S Stat Calculations, Linear Regression (a + bx), enter . You should then see a dialogue
box. In the drop-down boxes, arrow down to miles for the X
List:, then press tab and arrow down to price for the Y List:.
tab to OK and press enter .
I
3. Press ctrl
and use the Navpad to arrow to Add Data &
Statistics. Press enter .
4. Press tab to select the “Click to add variable” for the horizontal
axis. Arrow to points and press enter to select it.
The linear regression information, a, b, r2, r, and resid will be
displayed in another column within the Lists & Spreadsheet page.
5. Press tab again and the box will move to the vertical axis. ­Select
wins. The data will now move into a scatterplot. TI-Nspire labels the x and y axes with the list names, making a well-labeled
graph to insert into documents.
6. Press ctrl to return to the Data & Statistics page. Press menu ;
arrow to ­Analyze S Regression S Show Linear (a + bx), and
press enter . The least-squares regression line along with the
equation will appear. If you arrow over the equation, the
will appear. Click and hold
. When the hand closes, , you
can move the equation using the arrow keys.
8. Least-squares regression lines on the calculator
Let’s use the Ford F-150 data to show how to find the equation
of the least-squares regression line on the TI-Nspire. Here are the
data.
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7. Save the document for later use. Press
document Truck prices.
ctrl
S
. Name your
9. Residual plots on the calculator
Let’s continue the analysis of the Ford F-150 miles driven and
price data from the previous Technology Corner. You should have
already made a scatterplot, calculated the equation of the leastsquares regression line, and graphed the line on your plot. Now
we want to make a residual plot.
1. Open the document Truck prices. Press ctrl N , arrow through
My Documents S Truck prices and press enter .
2. Press ctrl to go to the Data & Statistics page.
3. Press menu ; arrow to Analyze S Residuals S Show Residual
Plot. This will split the screen and the residual plot will be displayed below the graph of the least-squares regression line.
3. Name column A students. Arrow down to the formula cell and
press enter . students:= should appear. Type seq(x,x,1,1750)
and enter . This will put the digits 1 through 1750 in this list.
4. Name column B sampstudents. Arrow down to the formula
cell and press enter . sampstudents:= should appear. Type
randSamp(students,10,1) and press enter . This function will
take a random sample of 10 students from the list. “1” lets the
function know to do the sampling without replacement.
Note: Sampling with replacement is the default setting for this
function. You can use 0 as the third input in the randSamp command or close the parentheses after the second input.
Chapter 6 TI-Nspire Technology Corners
11. Analyzing random variables on the calculator
Chapter 4 TI-Nspire Technology Corner
10. Choosing an SRS
The TI-Nspire has a function called randSamp that will randomly
select individuals for a sample with or without replacement from
a population.
1. Check that your calculator’s random number generator is
­working properly.
• Open the Calculator Scratchpad by pressing
(or
A on the keypad).
• Type randint(1,1750) and press enter .
• Compare results with your classmates. If several students have
the same number, you’ll need to seed your calculator’s random
number generator with different numbers before you proceed.
Type randSeed, press
(to insert a space), type < last four
digits of your phone number> and press enter . Done should
appear. Now your calculator is ready to generate numbers that
are different from those of your classmates.
Let’s explore what the calculator can do using the random variable X = Apgar score of a randomly selected newborn from the
example on page 349.
1. Insert a Lists & Spreadsheet page. Press ctrl I , arrow to Add
Lists & Spreadsheet, and press enter .
• Name column A apgar and column B apgrprob.
• Enter the values of the random variable (0 − 10) in the apgar
list and the corresponding probabilities in apgrprob.
2. Graph a histogram of the probability distribution.
• Insert a Data & Statistics page. Press ctrl I , arrow to Add
Data & Statistics, and press enter .
• Press ctrl menu and select Add X Variable with Summary
List. Press enter and a dialogue box should appear. a­ pgar
should be in the X List and apgrprob should be in the
­Summary List. If they are not, use the drop-down boxes to
select your variables. When your box looks like the one here,
tab to OK and press enter .
2. Insert a Lists & Spreadsheet page. If you already have a document open, press ctrl I and select Add Lists & Spreadsheet.
If you do not have a document already open, press
(
on the clickpad), then 4 . Press menu and select Add Lists &
Spreadsheet.
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The probability histogram should now be displayed.
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13. Binomial probability on the calculator
There are two handy commands on the TI-Nspire for finding
binomial probabilities:
binomPdf(n,p,k) computes P(X = k)
binomCdf(n,p,k) computes P(X ≤ k)
3. To calculate the mean and standard deviation of the random
variable, use one-variable statistics with apgar as the Data List
and apgrprob as the Frequency List.
• Press ctrl to go back to the Lists & Spreadsheet page.
• Press menu S Statistics S Stat Calculations S OneVariable Statistics.
• Make sure your X1 List, Frequency List, and 1st Result Column
have the variables/values shown (you can press the down arrow in the drop-down boxes to access the variable names and
type C for 1st Result Column). tab to OK and press enter .
You will need to open the Calculator Scratchpad (press
or
A on the clickpad). These two commands can be found
in the Distributions menu within the Statistics menu. You can
access them by pressing menu S Statistics S Distributions. A
dialogue box will appear. Input n (the number of observations), p
(probability of success), and k (number of successes).
For the parents having n = 5 children, each with probability
p = 0.25 of type O blood:
P(X = 3) = binomPdf(5,0.25,3) = 0.08789
To find P(X > 3), we used the complement rule:
P(X > 3) = 1 − P(X ≤ 3) = 1 − binomCdf(5,0.25,3)
= 0.01563
• The statistics should now be displayed in your Lists & Spreadsheet page.
Of course, we could also have done this as
P(X > 3) = P(X = 4) + P(X = 5)
= binomPdf(5,0.25,4) +
binomPdf(5,0.25,5)
= 0.01465 + 0.00098 = 0.01563
On the TI-Nspire, you can also calculate using
P(X > 3) = P(X = 4) + P(X = 5)
= binomCdf(5,0.25,4,5)
= 0.01563
12. Binomial coefficients on the calculator
5
To calculate a binomial coefficient like a b on the TI-Nspire,
2
proceed as follows. Open the Calculator Scratchpad by pressing
A on the clickpad). Press menu S Probability
(or
S Combinations, and then enter . nCr( will appear. Complete
the command nCr(5,2) and press enter .
14. Geometric probability on the calculator
There are two handy commands on the TI-Nspire for finding
geometric probabilities:
geomPdf(p,k) computes P(Y = k)
geomCdf(p,k) computes P(Y ≤ k)
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You will need to open the Calculator Scratchpad (press
or
A ). These two commands can be found in the Distributions
menu within the Statistics menu. You can access them by pressing
menu
S Statistics S Distributions. A dialogue box will appear.
Input p (probability of success) and k (number of trials to get the
first success).
16. Inverse t on the calculator
For the Lucky Day Game, with probability of success p = 17 on
each trial,
P(Y = 10) = geomPdf(1/7,10) = 0.0357
To find P(Y < 10), use geomCdf:
P(Y < 10) = P(Y ≤ 9) = geomCdf(1/7,9) = 0.7503
The TI-Nspire allows you to find critical values t* using the
inverse t command. As with the calculator’s inverse Normal command, you have to enter the area to the left of the desired critical
value. Let’s use the inverse t command to find the critical values
for parts (a) and (b) in the example on page 513.
A ) to insert a Calculator Scratchpad.
• Press
(or
• Press menu S Statistics S Distributions S Inverse t.
• A dialogue box will appear. For part (a), enter .025 for the
Area and 11 for the Deg of Freedom, df. tab to OK and press
enter .
For part (b), enter .05 for the Area and 47 for the Deg of Freedom,
df. tab to OK and press enter .
Chapter 8 TI-Nspire Technology Corners
15. Confidence interval for a population ­proportion
The TI-Nspire can be used to construct a confidence interval for
an unknown population proportion. We’ll demonstrate using the
example on page 500. Of n = 439 teens surveyed, x = 246 said
they thought young people should wait to have sex until after
marriage.
To construct a confidence interval:
A ) to insert a Calculator Scratchpad.
• Press
(
• Press menu S Statistics S Confidence Intervals S
1-Prop z Interval.
• A dialogue box will appear: Enter the values as shown below.
tab to OK and press enter .
• The critical values t* should now be displayed.
17. One-sample t intervals for m on the ­calculator
The lower and upper bounds of the confidence interval are
reported, along with the sample proportion p^ , the margin of error
(ME), and the sample size.
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Confidence intervals for a population mean using t procedures
can be constructed on the TI-Nspire, thus avoiding the use of
Table B. Here is a brief summary of the techniques when you
have only numerical summaries and when you have the actual
data values.
1. Using summary statistics: Auto pollution example, page 519
• Insert a Lists & Spreadsheet page: Press ctrl I and select
Add Lists & Spreadsheet.
• Press menu S Statistics S Confidence Intervals S t
interval.
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• The first dialogue box that appears asks for Data or Stats
in the drop-down box. Select Stats, tab to OK , and press
enter .
• In the next dialogue box, enter the values shown.
• tab to OK and press enter .
• The results should now appear in the spreadsheet.
Chapter 9 TI-Nspire Technology Corners
18. One-proportion z test on the calculator
The TI-Nspire can be used to test a claim about a population
proportion. We’ll demonstrate using the example on page 559.
In a random sample of size n = 500, the supervisor found x = 47
potatoes with blemishes. To perform a significance test:
A ) to insert a Calculator Scratchpad.
• Press
(or
• Press menu S Statistics S Stat Tests S 1-Prop z test.
• A dialogue box will appear. Enter the values shown: p0 = 0.08,
x = 47, and n = 500. Specify the alternative hypothesis as
“Ha: prop > p0 .” tab to OK and press enter .
Note: x is the number of successes and n is the number of trials.
Both must be whole numbers!
2. Using raw data: Video screen tension example, page 520
Enter the 20 video screen tension readings data using the following procedure.
• Insert a Lists & Spreadsheet page: Press ctrl I and select
Add Lists & Spreadsheet.
• Name the first column screen.
• Arrow down to the first cell and enter the 20 values.
You can see that the test statistic is z = 1.15392 and the P-value is
0.1243.
To construct the t interval:
• Press menu S Statistics S Confidence Intervals S t
interval.
• The first dialogue box that appears asks for Data or Stats in the
drop-down box. Select Data, tab to OK , and press enter .
• In the next dialogue box, select the data list, screen, tab to OK ,
and press enter .
To display the P-value as a shaded area under the Normal curve:
• Press
and select the Lists & Spreadsheet icon
.
• Press menu S Statistics S Stat Tests S 1-Prop z test.
• A dialogue box will appear: Enter the values shown below.
Check the box to Shade P Value. tab to OK and press enter .
• The results should now appear in the spreadsheet. (You may
have to scroll up to see them.)
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• The results should now appear in the spreadsheet.
19. Computing P-values from t distributions on the
calculator
You can use the tcdf command on the TI-Nspire to calculate areas
under a t distribution curve. The syntax is tcdf(lower bound,upper
bound,df). To use this command:
A ) to insert a Calculator Scratchpad.
• Press
(or
• Press menu S Statistics S Distributions S t Cdf.
• In the dialogue box that appears, enter your lower and upper
bound and degrees of freedom.
Use the t Cdf command to compute the P-values from the examples on pages 577 and 578.
• Better batteries: To find P(t ≥ 1.54), use Lower Bound: 1.54,
Upper Bound: 10000, and df:14.
• Two-sided test: To find the P-value for the two-sided test with
df = 36 and t = − 3.17, execute the command 2 # tCdf
(−10000,−3.17,36).
The test statistic is t = − 0.94 and the P-value is 0.1809.
If you check Shade P Value, you see a t-distribution curve
(df = 14) with the lower tail shaded.
If you are given summary statistics instead of the original data, you
would select the “Stats” option in the drop-down box.
Chapter 10 TI-Nspire Technology Corners
21. Confidence interval for a difference in ­proportions
20. One-sample t test for a mean on the ­calculator
You can perform a one-sample t test using either raw data or
summary statistics on the TI-Nspire. Let’s use the calculator to
carry out the test of H0: m = 5 versus Ha: m < 5 from the dissolved
oxygen example on page 580.
Start by entering the sample data into a column in a Lists &
Spreadsheet page. Name the column oxygen. Then, to do the test:
• Press menu S Statistics S Stats Tests S t Test.
• The first dialogue box that appears asks for Data or Stats in
the drop-down box. Make sure Data is selected. tab to OK
and press enter .
• In the next dialogue box, enter the values shown in the following box. To just “calculate,” leave the Shade PValue option
unchecked. Then tab to OK and press enter .
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The TI-Nspire can be used to construct a confidence interval for
p1 − p2 . We’ll demonstrate using the example on page 617. Of
n1 = 799 teens surveyed, X = 639 said they used social networking
sites. Of n2 = 2253 adults surveyed, X = 1555 said they engaged
in social networking. To construct a confidence interval:
A ) to insert a Calculator Scratchpad.
(
• Press
• Press menu S Statistics S Confidence Intervals S
2-Prop z Interval.
• A dialogue box will appear. Enter the values shown below.
tab to OK and press enter .
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22. Significance test for a difference in ­proportions
The TI-Nspire can be used to perform significance tests for comparing two proportions. Here, we use the data from the Hungry
Children example on page 622.
To perform a test of H0: p1 − p2 = 0:
A ) to insert a Calculator Scratchpad.
(or
• Press
• Press menu S Statistics S Stat Tests S 2-Prop z test.
• A dialogue box will appear. Enter the values shown: x1 = 19,
n1 = 80, x2 = 26, n2 = 150. Specify the alternative hypothesis
Ha: p1 ≠ p2 as shown.
• tab to OK and press enter .
23. Two-sample t intervals on the calculator
You can use the two-sample t interval command on the TI-Nspire
to construct a confidence interval for the difference between two
means. We’ll show you the steps using the summary statistics from
the pine trees example on page 641.
A ) to insert a Calculator Scratchpad.
• Press
(or
• Press menu S Statistics S Confidence Intervals S
2-Sample t interval.
• In the first dialogue box, select Stats in the drop-down menu.
tab to OK and press enter . Another dialogue box will appear.
• Enter the summary statistics shown:
You will see that the z statistic is z = 1.168 and the P-value is
0.2427, as shown here. Do you see the combined proportion of
students who didn’t eat breakfast? It’s the p^ value, 0.1957.
• Enter the confidence level: C level: .90. For pooled: choose
“No.” (We’ll discuss pooling later.) tab to OK and press enter .
To display the P-value as a shaded area under the standard
Normal curve:
• Press
and select the Lists & Spreadsheet icon
.
• Press menu S Statistics S Stat Tests S 2-Prop z test. A
dialogue box will appear.
• Enter the values shown in the following box. Check the box
to Shade P Value. tab to OK and press enter .
Starnes-Yates5e_AppB_A05-A20hr.indd 15
11/22/13 10:49 AM
A-16
A p p e n d i x B T I - N s p i r e tm Te c h n o l o g y C o r n e r s
24. Two-sample t tests on the calculator
Technology gives smaller P-values for two-sample t tests than the
conservative method. That’s because calculators and software
use the more complicated formula on page 640 to obtain a larger
number of degrees of freedom.
Start by entering the sample data into a column in a Lists &
Spreadsheet page. Name column A calcium and enter the Group
1 data. Name column B placebo and enter the Group 2 data.
Then do the test:
• Press menu S Statistics S Stats Tests S 2-Sample t Test.
• In the first dialogue box, select Data in the drop-down menu.
tab to OK and press enter .
• In the next dialogue box, enter the values shown, tab to OK ,
and press enter .
between c2 = 10.180 and a very large number (we’ll use 10,000)
under the chi-square density curve with 5 degrees of freedom.
• Press
and the Calculator Scratchpad should appear.
• Press menu S Statistics S Distributions S c2 Cdf.
• In the dialogue box that appears, enter the values shown in
the following box. tab to OK and press enter .
As the calculator screen shot shows, this method gives a more
precise P-value than Table C.
Note: To just “calculate,” leave the Shade P value option unchecked.
• The results should now appear in the spreadsheet.
26. Chi-square test for goodness of fit on the calculator
You can use the TI-Nspire to perform the calculations for a chisquare test for goodness of fit. We’ll use the data from the hockey
and birthdays example on page 688 to illustrate the steps.
1. Enter the observed counts and expected counts in two separate
columns in a Lists & Spreadsheet page. Name the columns observed and expected.
Birthday
If you check the Shade P value box, the appropriate t distribution will also be displayed, showing the same results and the
shaded area corresponding to the P-value.
Observed Expected
Jan-Mar
32
20
Apr-June
20
20
July-Aug
16
20
Sept-Dec
12
20
2. Perform a chi-square test for goodness of fit.
• Press menu S Statistics S Stat Tests S c2 GOF.
• In the dialogue box that appears, enter the values shown in
the following box. tab to OK and press enter .
If you leave the Shade P value box unchecked, you’ll get the test
results within the spreadsheet containing the test statistic, P-value,
and df. If you check the Shade P value box, you’ll get a picture
of the appropriate chi-square distribution with the test statistic
marked and shaded area corresponding to the P-value.
Chapter 11 TI-Nspire Technology Corners
25. Finding P-values for chi-square tests on the calculator
To find the P-value in the M&M’S® example on page 685 with
your calculator, use the c2 cdf command. We ask for the area
Starnes-Yates5e_AppB_A05-A20hr.indd 16
11/22/13 10:49 AM
C h a p t e r 1 1 T I - N s p i r e TM Te c h n o l o g y C o r n e r s
We’ll discuss the Comp List results later.
27. Chi-square tests for two-way tables on the calculator
You can use the TI-Nspire to perform calculations for a chi-square
test for homogeneity. We’ll use the data from the restaurant study
on page 704 to illustrate the process.
A ) to insert a Calculator Scratchpad.
1. Press
(
2. Define a matrix by doing the following:
• Name your matrix by typing musicinfluence ctrl
.A
box will appear with different math type options. Select
and
enter “3” for Number of rows and “3” for Number of columns.
• Type in the corresponding row data, pressing
entries. Press enter when finished.
tab
A-17
4. To see the expected counts and component matrix, press var
and select stat.expmatrix for the expected matrix or stat.compmatrix for the component matrix.
between
Chapter 12 TI-Nspire Technology Corners
28. Confidence interval for slope on the
calculator
3. To perform the chi-square test, do the following steps:
• Press menu S Statistics S Stat tests S c2 2-way Test.
• Specify the observed matrix, tab to OK , and press enter .
• The results will be displayed and the expected matrix and
component matrix will be calculated.
Starnes-Yates5e_AppB_A05-A20hr.indd 17
Let’s use the data from the Ford F-150 truck example on page A-9
to construct a confidence interval for the slope of a population
(true) regression line on the TI-Nspire.
1. Insert a Lists & Spreadsheet page, and name column A miles
and column B price. Type the corresponding values into each
column.
2. To construct a confidence interval:
• Press menu S Statistics S Confidence Intervals S Linear Reg t Intervals.
• In the first dialogue box, select Slope. tab to OK and press
enter .
11/22/13 10:49 AM
A-18
A p p e n d i x B T I - N s p i r e tm Te c h n o l o g y C o r n e r s
• In the next dialogue box, select miles for the X List and price
for the Y List. Enter the rest of the values shown. tab to OK
and press enter .
30. Transforming to achieve linearity on the calculator
We’ll use the planet data on page 779 to illustrate a general
strategy for performing transformations with logarithms on the
TI-Nspire. A similar approach could be used for transforming data
with powers and roots.
1. Insert a Lists & Spreadsheet page, and name column A distance
and column B period. Type the corresponding values into each
column.
2. Make a scatterplot of y versus x and confirm that there is a
curved pattern.
• Insert a Data & Statistics page. Press ctrl I and select Add
Data & Statistics.
• Press tab and select distance for the horizontal axis. Press
tab again and select period for the vertical axis.
29. Significance test for slope on the calculator
Let’s use the data from the crying and IQ study on page 754 to
perform a significance test for the slope of the population regression line on the TI-Nspire.
1. Insert a Lists & Spreadsheet page, and name column A crycount
and column B iqscore. Type the corresponding values into each
column.
2. To do a significance test:
• Press menu S Statistics S Stat Tests S Linear Reg t Test.
• Select crycount for the X List and iqscore for the Y List. Enter
the rest of the values as shown. tab to OK and press enter .
Starnes-Yates5e_AppB_A05-A20hr1.indd 18
3. To “straighten” the curve (that is, determine the relationship),
we can use different models of the explanatory-response data to
see which one provides a linear relationship.
• Press ctrl
to return your spreadsheet. Name column c
lndistance and column d lnperiod.
• In the formula cell for lndistance, press enter and enter
ln(distance) to take the natural log of the distance values.
• Repeat this step for lnperiod using the period data.
4. To see if an exponential model fits the data:
• Insert another Data & Statistics page.
• Put distance on the horizontal axis and lnperiod on the vertical axis. If the relationship looks linear, then an exponential
model is appropriate.
11/25/13 2:25 PM
C h a p t e r 1 2 T I - N s p i r e TM Te c h n o l o g y C o r n e r s
5. To see if a power model fits the data:
• Using the same Data & Statistics page, change the horizontal
axis to lndistance.
• If this relationship looks linear, then a power model is
appropriate.
6. If a linear pattern is present, calculate the equation of the leastsquares regression line:
• In the spreadsheet, press menu S Statistics S Calculations S Linear Regression(a + bx).
• In the dialogue box, select lndistance for X List, lnperiod for
Y List, and enter the rest of the values as shown. tab to OK
and press enter .
Starnes-Yates5e_AppB_A05-A20hr.indd 19
A-19
7. Construct a residual plot to look for any departures from the
linear pattern.
• Insert another Data & Statistics page.
• For the horizontal axis select lndistance. For Ylist, use the
stat.resid list stored in the calculator.
8. To make a prediction for a specific value of the explanatory variable, compute log(x) or ln(x), if appropriate. Then do f1(k) to
obtain the predicted value of log y or ln y. To get the predicted
value of y, do 10^Ans or e^Ans to undo the logarithm transformation. Here’s our prediction of the period of revolution for
Eris, which is at a distance of 102.15 AU from the sun.
11/22/13 10:49 AM
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Glossary/Glosario
G-1
Formulas for AP® Statistics Exam
Students are provided with the following formulas on both the
multiple choice and free-response sections of the AP® Statistics
exam.
I. Descriptive Statistics
∙x
x=
m −x = m
s −x =
i
n
s
"n
III. Inferential Statistics
1
sx =
∙ (xi − x)2
Ån − 1
Standardized test statistic:
(n1 − 1)s21 + (n2 − 1)s22
sp =
Ç (n1 − 1) + (n2 − 1)
y^ = b0 + b1x
b1 =
If x is the mean of a random sample of size n from an infinite population with mean m and standard deviation s, then:
∙ (xi − x)(yi − y)
∙ (xi − x)2
statistic − parameter
standard deviation of statistic
Confidence interval: statistic ± (critical value) ∙ (std. deviation of statistic)
Single-Sample
Statistic
Sample Mean
Standard Deviation of Statistic
s
"n
b0 = y − b1x
xi − x yi − y
1
r=
a
ba
b
∙
sx
sy
n−1
b1 = r
sy
sx
sb1 =
s21 s22
+
Å n1 n2
2
Special case when
s1 = s2
II. Probability
s
P(A c B) = P(A) + P(B) − P(A d B)
P(A 0 B) =
P(A d B)
P(B)
Difference of
sample proportions
E(X) = mx = ∙ xipi
Var(X) =
s2x
Å
= ∙ (xi − mx) pi
2
If X has a binomial distribution with parameters n and p, then:
n
P(X = k) = a bpk(1 − p)n−k
k
mx = np
p (1 − p)
n
Standard Deviation of Statistic
Difference of
sample means
n−2
$ ∙ (xi − x)
Å
Two-Sample
Statistic
∙ (yi − y^ i)2
Ç
Sample Proportion
1
1
+
Å n1 n2
p1(1 − p1) p2(1 − p2)
+
n1
n2
Special case when
p1 = p2
"p (1 − p)
Chi-square test statistic =
∙
1
1
+ Å n1 n2
(observed − expected)2
expected
sx = "np(1 − p)
mp^ = p
sp^ =
p(1 − p)
Å
n
Starnes-Yates5e_Formulas_hr.indd 1
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This page intentionally left blank
Probability
z
Table entry for z is the area under the standard Normal curve to the left of z.
Table A Standard Normal probabilities
z
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
-3.4
-3.3
-3.2
-3.1
-3.0
-2.9
-2.8
-2.7
-2.6
-2.5
-2.4
-2.3
-2.2
-2.1
-2.0
-1.9
-1.8
-1.7
-1.6
-1.5
.0003
.0005
.0007
.0010
.0013
.0019
.0026
.0035
.0047
.0062
.0082
.0107
.0139
.0179
.0228
.0287
.0359
.0446
.0548
.0668
.0003
.0005
.0007
.0009
.0013
.0018
.0025
.0034
.0045
.0060
.0080
.0104
.0136
.0174
.0222
.0281
.0351
.0436
.0537
.0655
.0003
.0005
.0006
.0009
.0013
.0018
.0024
.0033
.0044
.0059
.0078
.0102
.0132
.0170
.0217
.0274
.0344
.0427
.0526
.0643
.0003
.0004
.0006
.0009
.0012
.0017
.0023
.0032
.0043
.0057
.0075
.0099
.0129
.0166
.0212
.0268
.0336
.0418
.0516
.0630
.0003
.0004
.0006
.0008
.0012
.0016
.0023
.0031
.0041
.0055
.0073
.0096
.0125
.0162
.0207
.0262
.0329
.0409
.0505
.0618
.0003
.0004
.0006
.0008
.0011
.0016
.0022
.0030
.0040
.0054
.0071
.0094
.0122
.0158
.0202
.0256
.0322
.0401
.0495
.0606
.0003
.0004
.0006
.0008
.0011
.0015
.0021
.0029
.0039
.0052
.0069
.0091
.0119
.0154
.0197
.0250
.0314
.0392
.0485
.0594
.0003
.0004
.0005
.0008
.0011
.0015
.0021
.0028
.0038
.0051
.0068
.0089
.0116
.0150
.0192
.0244
.0307
.0384
.0475
.0582
.0003
.0004
.0005
.0007
.0010
.0014
.0020
.0027
.0037
.0049
.0066
.0087
.0113
.0146
.0188
.0239
.0301
.0375
.0465
.0571
.0002
.0003
.0005
.0007
.0010
.0014
.0019
.0026
.0036
.0048
.0064
.0084
.0110
.0143
.0183
.0233
.0294
.0367
.0455
.0559
-1.4
-1.3
-1.2
-1.1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
.0808
.0968
.1151
.1357
.1587
.1841
.2119
.2420
.2743
.3085
.3446
.3821
.4207
.0793
.0951
.1131
.1335
.1562
.1814
.2090
.2389
.2709
.3050
.3409
.3783
.4168
.0778
.0934
.1112
.1314
.1539
.1788
.2061
.2358
.2676
.3015
.3372
.3745
.4129
.0764
.0918
.1093
.1292
.1515
.1762
.2033
.2327
.2643
.2981
.3336
.3707
.4090
.0749
.0901
.1075
.1271
.1492
.1736
.2005
.2296
.2611
.2946
.3300
.3669
.4052
.0735
.0885
.1056
.1251
.1469
.1711
.1977
.2266
.2578
.2912
.3264
.3632
.4013
.0721
.0869
.1038
.1230
.1446
.1685
.1949
.2236
.2546
.2877
.3228
.3594
.3974
.0708
.0853
.1020
.1210
.1423
.1660
.1922
.2206
.2514
.2843
.3192
.3557
.3936
.0694
.0838
.1003
.1190
.1401
.1635
.1894
.2177
.2483
.2810
.3156
.3520
.3897
.0681
.0823
.0985
.1170
.1379
.1611
.1867
.2148
.2451
.2776
.3121
.3483
.3859
-0.1
-0.0
.4602
.5000
.4562
.4960
.4522
.4920
.4483
.4880
.4443
.4840
.4404
.4801
.4364
.4761
.4325
.4721
.4286
.4681
.4247
.4641
(Continued)
Starnes-Yates5e_Tables_001_005hr.indd 1
12/9/13 5:54 PM
T-2
Ta b l e s
Probability
z
Table entry for z is the area under the standard Normal curve to the left of z.
Table A Standard Normal probabilities (continued)
z
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.5000
.5398
.5793
.6179
.6554
.6915
.7257
.7580
.7881
.8159
.8413
.8643
.8849
.9032
.9192
.9332
.9452
.9554
.9641
.9713
.9772
.9821
.9861
.9893
.9918
.9938
.9953
.9965
.9974
.9981
.9987
.9990
.9993
.9995
.9997
.5040
.5438
.5832
.6217
.6591
.6950
.7291
.7611
.7910
.8186
.8438
.8665
.8869
.9049
.9207
.9345
.9463
.9564
.9649
.9719
.9778
.9826
.9864
.9896
.9920
.9940
.9955
.9966
.9975
.9982
.9987
.9991
.9993
.9995
.9997
.5080
.5478
.5871
.6255
.6628
.6985
.7324
.7642
.7939
.8212
.8461
.8686
.8888
.9066
.9222
.9357
.9474
.9573
.9656
.9726
.9783
.9830
.9868
.9898
.9922
.9941
.9956
.9967
.9976
.9982
.9987
.9991
.9994
.9995
.9997
.5120
.5517
.5910
.6293
.6664
.7019
.7357
.7673
.7967
.8238
.8485
.8708
.8907
.9082
.9236
.9370
.9484
.9582
.9664
.9732
.9788
.9834
.9871
.9901
.9925
.9943
.9957
.9968
.9977
.9983
.9988
.9991
.9994
.9996
.9997
.5160
.5557
.5948
.6331
.6700
.7054
.7389
.7704
.7995
.8264
.8508
.8729
.8925
.9099
.9251
.9382
.9495
.9591
.9671
.9738
.9793
.9838
.9875
.9904
.9927
.9945
.9959
.9969
.9977
.9984
.9988
.9992
.9994
.9996
.9997
.5199
.5596
.5987
.6368
.6736
.7088
.7422
.7734
.8023
.8289
.8531
.8749
.8944
.9115
.9265
.9394
.9505
.9599
.9678
.9744
.9798
.9842
.9878
.9906
.9929
.9946
.9960
.9970
.9978
.9984
.9989
.9992
.9994
.9996
.9997
.5239
.5636
.6026
.6406
.6772
.7123
.7454
.7764
.8051
.8315
.8554
.8770
.8962
.9131
.9279
.9406
.9515
.9608
.9686
.9750
.9803
.9846
.9881
.9909
.9931
.9948
.9961
.9971
.9979
.9985
.9989
.9992
.9994
.9996
.9997
.5279
.5675
.6064
.6443
.6808
.7157
.7486
.7794
.8078
.8340
.8577
.8790
.8980
.9147
.9292
.9418
.9525
.9616
.9693
.9756
.9808
.9850
.9884
.9911
.9932
.9949
.9962
.9972
.9979
.9985
.9989
.9992
.9995
.9996
.9997
.5319
.5714
.6103
.6480
.6844
.7190
.7517
.7823
.8106
.8365
.8599
.8810
.8997
.9162
.9306
.9429
.9535
.9625
.9699
.9761
.9812
.9854
.9887
.9913
.9934
.9951
.9963
.9973
.9980
.9986
.9990
.9993
.9995
.9996
.9997
.5359
.5753
.6141
.6517
.6879
.7224
.7549
.7852
.8133
.8389
.8621
.8830
.9015
.9177
.9319
.9441
.9545
.9633
.9706
.9767
.9817
.9857
.9890
.9916
.9936
.9952
.9964
.9974
.9981
.9986
.9990
.9993
.9995
.9997
.9998
Starnes-Yates5e_Tables_001_005hr.indd 2
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Ta b l e s
T-3
Probability
p
Table entry for p and C is the point t* with probability p lying to its right
and probability C lying between −t* and t*.
t*
Table B t distribution critical values
df
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
40
50
60
80
100
1000
∞
.25
1.000
0.816
0.765
0.741
0.727
0.718
0.711
0.706
0.703
0.700
0.697
0.695
0.694
0.692
0.691
0.690
0.689
0.688
0.688
0.687
0.686
0.686
0.685
0.685
0.684
0.684
0.684
0.683
0.683
0.683
0.681
0.679
0.679
0.678
0.677
0.675
0.674
.20
1.376
1.061
0.978
0.941
0.920
0.906
0.896
0.889
0.883
0.879
0.876
0.873
0.870
0.868
0.866
0.865
0.863
0.862
0.861
0.860
0.859
0.858
0.858
0.857
0.856
0.856
0.855
0.855
0.854
0.854
0.851
0.849
0.848
0.846
0.845
0.842
0.841
.15
1.963
1.386
1.250
1.190
1.156
1.134
1.119
1.108
1.100
1.093
1.088
1.083
1.079
1.076
1.074
1.071
1.069
1.067
1.066
1.064
1.063
1.061
1.060
1.059
1.058
1.058
1.057
1.056
1.055
1.055
1.050
1.047
1.045
1.043
1.042
1.037
1.036
.10
3.078
1.886
1.638
1.533
1.476
1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.303
1.299
1.296
1.292
1.290
1.282
1.282
.05
6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746
1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
1.684
1.676
1.671
1.664
1.660
1.646
1.645
50%
60%
70%
80%
90%
Starnes-Yates5e_Tables_001_005hr.indd 3
Tail probability p
.025
.02
12.71
15.89
4.303
4.849
3.182
3.482
2.776
2.999
2.571
2.757
2.447
2.612
2.365
2.517
2.306
2.449
2.262
2.398
2.228
2.359
2.201
2.328
2.179
2.303
2.160
2.282
2.145
2.264
2.131
2.249
2.120
2.235
2.110
2.224
2.101
2.214
2.093
2.205
2.086
2.197
2.080
2.189
2.074
2.183
2.069
2.177
2.064
2.172
2.060
2.167
2.056
2.162
2.052
2.158
2.048
2.154
2.045
2.150
2.042
2.147
2.021
2.123
2.009
2.109
2.000
2.099
1.990
2.088
1.984
2.081
1.962
2.056
1.960
2.054
95%
96%
Confidence level C
.01
31.82
6.965
4.541
3.747
3.365
3.143
2.998
2.896
2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.423
2.403
2.390
2.374
2.364
2.330
2.326
.005
63.66
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861
2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
2.704
2.678
2.660
2.639
2.626
2.581
2.576
.0025
127.3
14.09
7.453
5.598
4.773
4.317
4.029
3.833
3.690
3.581
3.497
3.428
3.372
3.326
3.286
3.252
3.222
3.197
3.174
3.153
3.135
3.119
3.104
3.091
3.078
3.067
3.057
3.047
3.038
3.030
2.971
2.937
2.915
2.887
2.871
2.813
2.807
.001
318.3
22.33
10.21
7.173
5.893
5.208
4.785
4.501
4.297
4.144
4.025
3.930
3.852
3.787
3.733
3.686
3.646
3.611
3.579
3.552
3.527
3.505
3.485
3.467
3.450
3.435
3.421
3.408
3.396
3.385
3.307
3.261
3.232
3.195
3.174
3.098
3.091
.0005
636.6
31.60
12.92
8.610
6.869
5.959
5.408
5.041
4.781
4.587
4.437
4.318
4.221
4.140
4.073
4.015
3.965
3.922
3.883
3.850
3.819
3.792
3.768
3.745
3.725
3.707
3.690
3.674
3.659
3.646
3.551
3.496
3.460
3.416
3.390
3.300
3.291
98%
99%
99.5%
99.8%
99.9%
12/9/13 5:54 PM
T-4
Ta b l e s
Probability
p
2
Table entry for p is the point c2 with probability p lying to its right.
Table C Chi−square distribution critical values
Tail probability p
df
.25
.20
.15
.10
.05
1
1.32
1.64
2.07
2.71
3.84
2
2.77
3.22
3.79
4.61
3
4.11
4.64
5.32
6.25
4
5.39
5.99
6.74
5
6.63
7.29
8.12
6
7.84
8.56
.025
.02
.01
.005
5.02
5.41
6.63
7.88
5.99
7.38
7.82
9.21
7.81
9.35
9.84
11.34
7.78
9.49
11.14
11.67
9.24
11.07
12.83
13.39
9.45
10.64
12.59
14.45
.0025
.001
.0005
9.14
10.83
12.12
10.60
11.98
13.82
15.20
12.84
14.32
16.27
17.73
13.28
14.86
16.42
18.47
20.00
15.09
16.75
18.39
20.51
22.11
15.03
16.81
18.55
20.25
22.46
24.10
7
9.04
9.80
10.75
12.02
14.07
16.01
16.62
18.48
20.28
22.04
24.32
26.02
8
10.22
11.03
12.03
13.36
15.51
17.53
18.17
20.09
21.95
23.77
26.12
27.87
9
11.39
12.24
13.29
14.68
16.92
19.02
19.68
21.67
23.59
25.46
27.88
29.67
10
12.55
13.44
14.53
15.99
18.31
20.48
21.16
23.21
25.19
27.11
29.59
31.42
11
13.70
14.63
15.77
17.28
19.68
21.92
22.62
24.72
26.76
28.73
31.26
33.14
12
14.85
15.81
16.99
18.55
21.03
23.34
24.05
26.22
28.30
30.32
32.91
34.82
13
15.98
16.98
18.20
19.81
22.36
24.74
25.47
27.69
29.82
31.88
34.53
36.48
14
17.12
18.15
19.41
21.06
23.68
26.12
26.87
29.14
31.32
33.43
36.12
38.11
15
18.25
19.31
20.60
22.31
25.00
27.49
28.26
30.58
32.80
34.95
37.70
39.72
16
19.37
20.47
21.79
23.54
26.30
28.85
29.63
32.00
34.27
36.46
39.25
41.31
17
20.49
21.61
22.98
24.77
27.59
30.19
31.00
33.41
35.72
37.95
40.79
42.88
18
21.60
22.76
24.16
25.99
28.87
31.53
32.35
34.81
37.16
39.42
42.31
44.43
19
22.72
23.90
25.33
27.20
30.14
32.85
33.69
36.19
38.58
40.88
43.82
45.97
20
23.83
25.04
26.50
28.41
31.41
34.17
35.02
37.57
40.00
42.34
45.31
47.50
21
24.93
26.17
27.66
29.62
32.67
35.48
36.34
38.93
41.40
43.78
46.80
49.01
22
26.04
27.30
28.82
30.81
33.92
36.78
37.66
40.29
42.80
45.20
48.27
50.51
23
27.14
28.43
29.98
32.01
35.17
38.08
38.97
41.64
44.18
46.62
49.73
52.00
24
28.24
29.55
31.13
33.20
36.42
39.36
40.27
42.98
45.56
48.03
51.18
53.48
25
29.34
30.68
32.28
34.38
37.65
40.65
41.57
44.31
46.93
49.44
52.62
54.95
26
30.43
31.79
33.43
35.56
38.89
41.92
42.86
45.64
48.29
50.83
54.05
56.41
27
31.53
32.91
34.57
36.74
40.11
43.19
44.14
46.96
49.64
52.22
55.48
57.86
28
32.62
34.03
35.71
37.92
41.34
44.46
45.42
48.28
50.99
53.59
56.89
59.30
29
33.71
35.14
36.85
39.09
42.56
45.72
46.69
49.59
52.34
54.97
58.30
60.73
30
34.80
36.25
37.99
40.26
43.77
46.98
47.96
50.89
53.67
56.33
59.70
62.16
40
45.62
47.27
49.24
51.81
55.76
59.34
60.44
63.69
66.77
69.70
73.40
76.09
50
56.33
58.16
60.35
63.17
67.50
71.42
72.61
76.15
79.49
82.66
86.66
60
66.98
68.97
71.34
74.40
79.08
83.30
84.58
88.38
91.95
95.34
99.61
80
88.13
90.41
93.11
96.58
100
109.1
111.7
Starnes-Yates5e_Tables_001_005hr.indd 4
114.7
118.5
89.56
102.7
101.9
106.6
108.1
112.3
116.3
120.1
124.8
128.3
124.3
129.6
131.1
135.8
140.2
144.3
149.4
153.2
12/9/13 5:54 PM
Ta b l e s
T-5
Table D Random digits
Line
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
Starnes-Yates5e_Tables_001_005hr.indd 5
19223
73676
45467
52711
95592
68417
82739
60940
36009
38448
81486
59636
62568
45149
61041
14459
38167
73190
95857
35476
71487
13873
54580
71035
96746
96927
43909
15689
36759
69051
05007
68732
45740
27816
66925
08421
53645
66831
55588
12975
96767
72829
88565
62964
19687
37609
54973
00694
71546
07511
95034
47150
71709
38889
94007
35013
57890
72024
19365
48789
69487
88804
70206
32992
77684
26056
98532
32533
07118
55972
09984
81598
81507
09001
12149
19931
99477
14227
58984
64817
16632
55259
41807
78416
55658
44753
66812
68908
99404
13258
35964
50232
42628
88145
12633
59057
86278
05977
05233
88915
05756
99400
77558
93074
69971
15529
20807
17868
15412
18338
60513
04634
40325
75730
94322
31424
62183
04470
87664
39421
29077
95052
27102
43367
37823
36809
25330
06565
68288
87174
81194
84292
65561
18329
39100
77377
61421
40772
70708
13048
23822
97892
17797
83083
57857
66967
88737
19664
53946
41267
28713
01927
00095
60227
91481
72765
47511
24943
39638
24697
09297
71197
03699
66280
24709
80371
70632
29669
92099
65850
14863
90908
56027
49497
71868
74192
64359
14374
22913
09517
14873
08796
33302
21337
78458
28744
47836
21558
41098
45144
96012
63408
49376
69453
95806
83401
74351
65441
68743
16853
96409
27754
32863
40011
60779
85089
81676
61790
85453
39364
00412
19352
71080
03819
73698
65103
23417
84407
58806
04266
61683
73592
55892
72719
18442
77567
40085
13352
18638
84534
04197
43165
07051
35213
11206
75592
12609
47781
43563
72321
94591
77919
61762
46109
09931
60705
47500
20903
72460
84569
12531
42648
29485
85848
53791
57067
55300
90656
46816
42006
71238
73089
22553
56202
14526
62253
26185
90785
66979
35435
47052
75186
33063
96758
35119
88741
16925
49367
54303
06489
85576
93739
93623
37741
19876
08563
15373
33586
56934
81940
65194
44575
16953
59505
02150
02384
84552
62371
27601
79367
42544
82425
82226
48767
17297
50211
94383
87964
83485
76688
27649
84898
11486
02938
31893
50490
41448
65956
98624
43742
62224
87136
41842
27611
62103
48409
85117
81982
00795
87201
45195
31685
18132
04312
87151
79140
98481
79177
48394
00360
50842
24870
88604
69680
43163
90597
19909
22725
45403
32337
82853
36290
90056
52573
59335
47487
14893
18883
41979
08708
39950
45785
11776
70915
32592
61181
75532
86382
84826
11937
51025
95761
81868
91596
39244
41903
36071
87209
08727
97245
96565
97150
09547
68508
31260
92454
14592
06928
51719
02428
53372
04178
12724
00900
58636
93600
67181
53340
88692
03316
12/9/13 5:54 PM
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