Calculators and statistical software often use scientific notation to display numbers. The letter E (or e ) stands for exponent of 10:
2.3E+04 = 2 .
3 × 10 4 = 2 .
3 × 10 000 = 23 000
2.3E-04 = 2 .
3 × 10
− 4 = 2 .
3 × 1
10 000
= 0 .
00023
Sometimes the TI-84 returns an error message . If nothing else works, reset the memory: Mem → Reset → Reset RAM. Resetting erases lists you stored.
density = relative frequency (%) width of class interval sum of numbers in list average of a list of numbers = how many numbers there are in the list deviation from average = measurement − average
The standard deviation (SD) is the quadratic average ( root-mean-square ) of the deviations from the average:
SD = s sum of (deviations)
2 number of measurements
Shortcut formula for SD of a 0-1 list (p. 298):
SD of a 0-1 list = s fraction of ones
× fraction of zeroes standard score (p. 79) = how many SDs a value is above (+) or below ( − ) the average: value − average standard score of value =
SD
∗
Page numbers refer to Freedman, D., Pisani, R., & Purves, R. (2007).
Statistics (4th edition) . New York: Norton. STA201 Intermediate Statistics is equivalent to STA301 Statistics for Business and Economics.
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Descriptive statistics with the TI-84 :
Enter data in a list (e.g., L
1
): STAT → EDIT
STAT → CALC → 1-Var Stats L
1
¯ = ave, S x
Q1 = 25 th
= SD + , σ x
= SD, n percentile, Q3 = 75 th
= no. of measurements, percentile, Med = median
E (sum of draws) = (number of draws) × (average of box)
SE(sum of draws) =
√ number of draws × (SD of the box)
When the sample is reasonably large:
SE(sample percentage) ≈
SD of sample
√ sample size
× 100%
(compute SD of the sample using the shortcut formula for 0-1 lists)
SE(sample average) ≈
SD of sample
√ sample size
(only valid when the sample is large and random)
95% confidence interval for a parameter (general formula): point estimator ± 2 · (SE for estimator)
95% confidence interval for a population percentage : sample percentage ± 2 ·
SD of sample
√ sample size
× 100%
(compute SD of the sample using the shortcut formula for 0-1 lists)
TI-84 : STAT → TESTS → 1-PropZInt; x = number of times the event occurs
= sample percentage × sample size. To get percentages multiply the boundaries of the obtained confidence interval by 100%.
95% confidence interval for a population average : sample average ± 2 ·
SD of sample
√ sample size
TI-84 : STAT → TESTS → ZInterval (¯ = sample ave, σ x size)
= SD, n = sample
2

The test statistic says how many SEs away an observed value is from its expected value, where the expected value is calculated using the null hypothesis: test statistic = estimator − hypothetical value
SE for estimator
Large random sample: z -test
For large random samples, the test statistic approximately follows the standard normal curve; in that case the test statistic is written as z . To compute the observed significance level ( P -value) use the normal curve .
Area under standard normal curve with the TI-84 :
DISTR → normalcdf(lower boundary, upper boundary) e.g.
, area under standard normal curve to right of 1:
DISTR → normalcdf(1, 10
99
) z -test with TI-84 : STAT → TESTS → Z-Test
µ
0
= value of ave in null hypothesis (= 50 on p. 477), ¯ = sample ave, σ = SD, n = sample size. Select the appropriate alternative hypothesis: average of box is different from 50 ( = µ
0
), less than 50 ( < µ
0
), more than 50 ( > µ
0
).
Small random sample: t -test
For small random samples:
– use SD
+ instead of SD to compute the SE of the estimator:
SD
+
= s sample size sample size − 1
× SD
– when the histogram of the population doesn’t look too different from the normal curve, the test statistic approximately follows Student’s curve ; in that case the test statistic is written as t . To compute the p -value for a test on one average, use Student’s curve with degrees of freedom = sample size − 1
Area under Student’s curve with the TI-84 :
DISTR → tcdf(lower boundary, upper boundary, degrees of freedom) e.g.
, area under Student’s curve with 4 degrees of freedom to right of 2.2:
DISTR → tcdf(2.2, 10 99 , 4) t -test with TI-84 : STAT → TESTS → T-Test; as in Z-Test, with Sx = SD + ;
SD + is Sx obtained in STAT → CALC → 1-Var Stats L
1
.
Hypothesis test for a difference (pp. 503–506) test statistic = observed difference − hypothetical value of difference
SE for difference
SE for the difference of two independent quantities (p. 502):
SE for difference = p
(SE for first quantity) 2 + (SE for second quantity) 2
3

Correlation coefficient (p. 132). Convert each variable to standard units.
The average of the products gives the correlation coefficient: r = average of [( x in standard units) × ( y in standard units)]
Simple regression : line of best fit (p. 204): slope = r × SD of y
SD of x y -intercept = (ave of y ) − slope × (ave of x )
Correlation and simple regression with the TI-84 :
Enter data in two lists (e.g., x in L
1
, y in L
2
): STAT → EDIT
CATALOG → DiagnosticOn → ENTER → ENTER
STAT → CALC → LinReg(ax+b) L
1
, L
2
( a = slope, b = intercept)
( x list first, y list second) confidence interval for slope: STAT → TESTS → LinRegTInt test for H
0 that slope = 0: STAT → TESTS → LinRegTTest
Multiple regression :
Statistical software provides a table with the estimated coefficients and SEs, and the test statistics and p -values for the null hypothesis (against a two-sided alternative) that the coefficients of the population regression function are equal to zero.
Chi-square test (pp. 525–506) test statistic = χ
2
= sum of
(observed frequency − hypothetical frequency) 2 hypothetical frequency
The p -value is approximately equal to the area to the right of the observed value for the χ 2 test statistic, under the χ 2 -curve with the appropriate number of degrees of freedom. When the model is fully specified (no parameters to estimate): degrees of freedom = (number of terms in χ
2
) − 1
Area under χ
2
-curve with the TI-84 :
DISTR → χ 2 cdf(lower boundary, upper boundary, degrees of freedom) e.g.
, area under χ 2 -curve with 5 degrees of freedom to the right of 14.2:
DISTR → χ 2 cdf(14.2, 10 99 , 5)
4