STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 1 week of September 3, turn in on or before September 11
Reading – The Roman-numbered prelude, and the Arabic-numbered through page 21 of the
text.
Written exercises to be turned in.
Note that in this, and subsequent assignments, some questions are labeled ‘do but don’t turn
in’. You should do and be sure you understand these exercises, as the issues they test can
appear in later tests. Do not however turn them in to be graded; you can check your answer
from the sample solution posted on the Web.
Page
13
21
23
28
30
33
Exercise
1.6
1.10
1.12
1.29
1.32
1.37
Histogram
Stem plot
Time plot
Bar chart of a categorical variable. Pareto chart
Recognize histogram shapes (Do this exercise, but do not turn it in)
Comparative (back-to-back) stem plot
Skills learned Introduction to uncontrolled variability and ‘standing back’ from a data set.
Drawing a bar chart, a histogram, a stem plot (aka stem and leaf display), and
a time plot.
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 2 week of September 10, turn in by September 18
Reading – Pages 37 to 82
Written exercises to be turned in
Page
50
55
59
63
74
74
75
80
80
83
85
Exercise
2.9
Do, but do not turn in. Check your answer from the back of the book.
2.12 Display the three groups in a comparative box and whisker plot, and comment
on the apparent impact of the logging.
2.31 Do, but do not turn in. Check your answer from the back of the book.
2.46 Calculate the five-number summary, and the values of the inner and outer
fences. Identify any players that are boxplot outliers.
3.6
Normal curves, the 68/95/99.7 rule.
3.7
Normal drill. Do, but do not turn in.
3.8
Comparison using normal scores.
3.10 Standard normal drill – direct
3.11 Standard normal drill. Do but do not turn in.
3.14 Standard normal drill – inverse
3.24 Using z scores to solve proportion questions.
Note. The chapter 3 assignments involve normal proportion calculations. Doing these
calculations is a mechanical skill that you get with practice; while it is a low-level skill it is a
vital one that, if not mastered now, will come back to haunt you later in the semester. In
this homework I ask you to turn in just a minimal number of calculations. However you
should do however many practice exercises (like those in Chapter 3) that it takes to develop
total fluency in working with tables and figuring proportions.
Skills learned: Numeric descriptive statistics; resistance; the five-number summary; the box
and whisker plot. A first look at the normal curve, used as a handy potential approximation
to a set of data. Skills of using a normal table.
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 3 week of September 17, turn in on or before September 25
Reading – Pages 91 to 125.
Written exercises to be turned in.
Do the calculations to three decimals. Using fewer than three decimals in these exercises can
make enough of a difference in the answers to be noticeable; using much more than three
decimals is probably overkill.
Page
96
101
110
101
Exercise
4.6
Draw and interpret a scatter plot.
4.8
Scatterplot, calculate correlation from definition and using calculator. (The
fourth exercise of this homework also uses this data set; you would be wise to
do the two sets of calculations at the same time to avoid having to rekey the
data.)
4.28 Scatterplot with repeated x; interpretation.
Continuing with the data of exercise 4.8, find the regression line to predict
forest lost from coffee price. Do this in two ways: (i) using the formula for
calculating the intercept and slope from the means, standard deviations and
correlation coefficients that you calculated for exercise 4.8; and (ii) using the
two-variable capability of your calculator. Re-draw the scatterplot you made
in the second exercise, and draw in the regression line on the plot. Us this to
predict the percent forest lost if the coffee price were to rise to 80 cents per
pound.
Skills learned: Bivariate data, Display with a scatterplot. Measuring strength of
association. What the correlation coefficient does and does not measure. The least squares
regression line. Fitting the regression line using a ‘statistical’ calculator.
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 4 week of September 24 to be turned in by October 2
Reminder. Your first in-class test takes the place of the scheduled lecture October 10
Reading – Pages 126 - 136, 149 – 160, 167 - 171
Written exercises to be turned in
1. The following data set shows the city and the highway fuel consumption of 22 cars of the
2002 model year. We’d like to know if we can predict the highway fuel consumption y using
the city fuel consumption x as a predictor
Car
AcuraNSX
AudiTTRoadster
AudiTTQuattro
BMWMCoupe
BMWZ3Coupe
BMWZ3Roadster
BMWZ8
ChevroletCorvette
ChryslerProwler
Ferrari360Modena
FordThunderbird
City
17
22
20
17
19
20
13
18
18
11
17
Highway
24
31
28
25
27
27
21
25
23
16
23
Car
HondaInsight
HondaS2000
LamborghiniMurcielago
MazdaMiata
Mercedes-BenzSL500
Mercedes-BenzSL600
Mercedes-BenzSLK230
Mercedes-BenzSLK320
Porsche911GT2
PorscheBoxster
ToyotaMR2
City
57
20
9
22
16
13
23
20
15
19
25
Highway
56
26
13
28
23
19
30
26
22
27
30
The numbers give the following summary statistics:
Variable
City
Highway
N
22
22
Mean
19.591
25.909
SD
9.2204
8.0469
Minimum
9
13
Maximum
57
56
The correlation between the two is 0.9808.
•
•
•
•
•
Page
160
162
Using these summary statistics, calculate the regression line to predict the highway
fuel consumption from the city fuel consumption.
Over what range of values can you interpolate using your line?
How do you interpret the intercept and the slope of this line? Do they make sense?
What would you predict to be the highway fuel consumption of a car with city fuel
consumption of 30 mpg?
Using your regression line, calculate the residuals and plot the residuals (vertical axis)
against the city gas mileage x. Comment on the plot generally, and on the Honda
Insight specifically.
Exercise
6.8
Simpson’s paradox
6.19-6.22 Working with a two-way table. Check the odd-numbered answers from the
back of the book.
Skills learned Fitting the regression line from the five bivariate summary numbers. Residual
plots, outliers, influence. Working with two-way tables of categorical data.
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 5 week of October 1, turn in on or before October 12 Note that this is an
automatic extension to the normal turning date, occasioned by your first in-term test on
October 10.
Reading – Pages 189 to 204
Written exercises to be turned in
Page
194
199
201
204
209
211
Exercise
8.6
Example – a mail-shot survey
8.10 Use Table B starting at line 139. Drawing a random sample using a table.
8.12 Explain clearly how you use the random number table. A stratified sample.
8.14 Non-response.
8.34 Cautions on reported behavior.
8.46 Effect of wording
Skills learned Use of random number tables, difficulties and issues in sampling.
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 6 week of October 8, turn in by the start of your recitation October 16
Reading – Pages 213 - 227
Written exercises.
Page
215
222
226
228
228
230
Exercise
9.2
Terms in experimentation
9.10 Meaning of the word ‘significant’
9.14 Describing a completely randomized experiment
9.16 Categorizing a study
9.18 Categorizing a study
9.28 Carry out the randomization for a CRD
Skills learned. Concepts and methods of designed experiments.
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 7 week of October 15, turn in no later than start of recitation October 23.
Reading – Pages 246 - 262
Written exercises to be turned in
Page
250
252
254
256
256
260
265
Exercise
10.4 Matching probability with event
10.6 Working with tetrahedral dice
10.8 A sample space
10.11 Don’t turn in – check at the back of the book. Benford’s Law
10.12 A discrete probability distribution
10.15 Don’t turn in – check at the back of the book. Normal probability calc.
10.32 Some probability calculations
Some normal table review. (Make sure you can do these exercises, but do not turn them in.)
Suppose the weight of aspirin tablets is normal with µ=325, σ=3 mg. What is the probability
that an individual tablet weighs:
1. less than 320 mg? (answer 0.0478)
2. less than 331 mg? (answer 0.9773)
3. between 331 and 320 mg? (answer 0.9295)
4. more than 318 mg? (answer 0.9902)
What is the weight that 99.9% of aspirin tablets exceed? (answer 315.7 mg)
What is the 90% normal range of weights if aspirin tablets? (answer 320 to 330 mg)
If you have any trouble with these calculations, review the material on using normal tables
that you will find on the class Web site.
Skills learned Rules of probability; discrete and continuous random variables
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 8 week of October 22, turn in on or before start of recitation October 30
Reading – Pages 271 - 287
Page
272
272
294
275
275
280
286
291
298
298
Exercise
11.2 Parameters and statistics
11.3 Parameters and statistics (do not turn in)
11.18 Parameters and statistics
11.4 Behavior of a mean as n increases.
11.5 Why insurance works (do not turn in)
11.8 Distribution of a sample mean. Effect of sample size
11.12 Individual values and sample mean
11.14 A Shewhart Xbar control chart
11.38 A normal probability calculation
11.42 Using CLT to solve problems involving a total
Skills learned: Sampling distribution of a mean. Central limit theorem. Introduction to
confidence intervals
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Reminder – the second mid-term test takes the place of the regular class on Wednesday
November 14
Homework 9 week of October 29. Turn-in date is November 6.
Reading – pages 343 – 355
Written exercises to be turned in
Page
348
352
354
357
357
357
357
359
Exercise
14.2 Interpreting a confidence interval.
14.6 A fuller analysis, from descriptives up to a CI.
14.8 Intervals with difference confidence levels.
14.13 Do not turn in – check answer at the back of the book
14.14 Confusion of CI with normal ranges
14.17 Do not turn in – relevance of sample size
14.18 Relevance of population size
14.28 A sample size calculation
Skills learned: Introduction to confidence intervals.
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 10 week of November 5, turn in on or before November 16
(Note that this is an automatic extension for this homework because of the second interm test, which is November 14.)
Reading – Pages 362 - 381
Written exercises to be turned in
Page
365
366
368
371
376
376
383
Exercise
15.2 Setting up null and alternative hypotheses and test statistic
15.4 Continuation
15.8 Evidence against the null
15.14 Calculating a one-sided P value
15.18 Get a test statistic and P value
15.20 A fuller example, including some calculations
15.40 Effect of sample size on P values.
Skills learned Some practical aspects of inferential procedures and cautions about taking the
numbers at face value.
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 11 week of November 12, turn in on or before November 20
Reading pages 387 - 397
Page
391
395
395
405
406
407
Exercise
16.2 A confidence interval with σ estimated from a large sample.
16.7 Do not turn in
16.8 A confidence interval and a test
16.20 Interpreting a description of a trial
16.24 Relevance of sample size
16.32 Assessment of evidence
Skills learned An overview of some further aspects of inference
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 12 week of November 19, turn in on or before November 27
Reading – Pages 433 - 446.
It is some time since you used your calculator for data analysis. Check your skills by finding
the mean and standard deviation of the numbers
2, 4, 6, 8, 10 (answer: mean = 6, standard deviation = 3.1623)
and the mixed-sign numbers
-3, -1, 1, 3, 5, 7 (answer: mean = 2, standard deviation = 3.7417)
If this gives you any trouble, review the material covered in homework 2 and your calculator
instruction manual.
Written exercises
From the text
Page Exercise
434
18.1 (Do not turn in) The standard error of the mean
436
18.3 (Do not turn in) Reading t tables
437
18.4 Reading t tables
438
18.6 A confidence interval for a normal mean. First step – you need to find the
mean and standard deviation of these numbers
439
18.7 (Do not turn in) Another confidence interval for a normal mean
448
18.13 (Do not turn in) A matched pairs t analysis and the impact of outliers
454
18.34 A matched pairs test
455
18.36 A confidence interval for a mean – precursor to a two-sample analysis
Skills learned The t distribution, origin and use; tables. Confidence intervals and tests on
small normal samples. Analysis of matched pairs data
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 13 week of November 26, turn in on or before December 4
Reading – Pages 461 - 473
Page
482
482
482
482
483
485
486
489
489
Exercise
19.22 Pick your technology
19.23 (do not turn in) continuation of technology pick
19.24 Pick your technology
19.27 (do not turn in) Assumptions for inference
19.28 Setting up two-sample hypotheses
19.37 (do not turn in) Two-sample analysis using original data.
19.40 Two-sample analysis given summary statistics. In addition to what the book
asks for, set up a 95% confidence interval for the difference in means.
19.48 Two-sample analysis using original data.
19.49 (do not turn in). Follow a test with a confidence interval.
Skills learned Two-sample inference on means
STAT 1001 Introduction to the Ideas of Statistics. Hawkins
Homework 14 week of December 3, turn in on or before December 11
This homework will not be turned back. The material on it is examinable
Reading – Pages 491 – 498, 502 – 507. (Ignore the section “Accurate confidence intervals
for a proportion”; we will not go down that road.)
Written exercises to be turned in.
From the text
Page Exercise
496
20.6 Conditions for a CI on a proportion
499 20.7 (do not turn in) Conditions for a CI for a proportion
499
20.8 Analysis of proportion data
503
20.14 A sample size calculation
507
20.18 Sampling distribution of a proportion
507
20.19 (do not turn in) Continuation
507
20.20 Continuation
508
20.21 (do not turn in) Continuation
508
20.22 Continuation
Not from the book
We want to test whether people really can generate plausible random
digits. Evidence is that most people give too many 3s and 7s, and not
enough 0s. We ask a volunteer to give us 200 random digits; of these
11 are zero. Use this piece of information to test the hypothesis that
the digits could be random.
Not from the book
We wonder whether a particular community has an unusual
distribution of blood type. In the whole US population, 45% have
Type O blood. We sample 400 individuals from the population and
150 have Type O blood. Is this evidence that they are different than
the population as a whole? Follow up the test with a 95% confidence
interval for the proportion of this community who have Type O blood.
Skills learned Inference on proportions in single sample.