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1. Chapter 9: Inferences from Two Samples
1. Among 843 smoking employees of hospitals with the smoking ban, 56 quit smoking
one year after the ban. Among 703 smoking employees from work places without
the smoking ban, 27 quit smoking a year after the ban.
a. Is there a significant difference between the two proportions? Use a 0.01
significance level.
b. Construct the 99% confidence interval for the difference between the two
proportions.
2. Company ''A'' claims that its yogurt cups contain, on average fewer calories than
that of a competitor. A sample of 50 such yogurt cups of company ''A'' produced
an average of 141 calories per cup with a standard deviation of 5.4 calories. A
sample of 40 yogurt cups of a rival company “B” produced an average of 144
calories per cup with a standard deviation of 6.3 calories.
a. Assuming that the calories of the yogurt cups for company “A” and company
“B” have Different Variances, use a 0.01 significance level to test the claim.
b. Calculate the p-value for the test of previous part & make a decision. Is this
decision in agreement with the previous one?
Statistics, Sample Test (Exam Review)
Module 4: Chapter 9 Review
Chapter 9: Inferences from Two Samples

2. c. Make the 98% confidence intervals for the difference between the two means.
3. Assuming that the calories of the yogurt cups for company “A” and company “B”
have Equal Variances, repeat the previous question.
4. Test a claim that weights of male college students have a larger variance than
female college students. (Use a significance level of 0.05 and assume the
populations are normal.)
: 31, 168, 28,
: 29, 125, 25
Males n x s
females n x s
= = =
= = =
5. Directional asymmetry (DA) is a phenomenon whereby in a population one side of
each organism is consistently larger than the other (I.E., left larger than right). An
evolutionary biologist studying DA measures the length of the left and right wings of
a sample of Drosophila (a type of flies, whose members are often called “small fruit
flies”) collected from nature and she gets these data.
a. The researcher decides to perform a two-sample t test to determine whether
the mean wing differs between the left and right sides of these flies. What
type of t test will she do? α = 0.05
b. Find the 90% confidence interval for the difference between the means.
Fly ID #
Length (MM)
Left wing
Length (MM)
Right wing
1 1.34 1.26
2 1 1.28
3 1.09 1.36
4 1.06 1.25
5 1.15 1.33
6 1.35 1.38
7 1.26 1.16
8 1.09 1.04
9 1.01 1.4
10 1.31 1.1
11 1.35 1.02
12 1.02 1.47
13 1.26 1.12
14 1.32 1.46

3. 15 1.29 1.24
16 1.02 1.41
17 1.2 1.38
6. An ecologist is concerned with whether pollution entering part of a preserve area is
compromising the health and growth of an endangered species of snake. To
determine this, he decides to measure the length of a set of mature adults from the
polluted area and an unpolluted area. The researcher decides to perform a two-
sample t test to determine whether the mean length of these snakes differs
between these two areas. α = 0.05
Length measurements
unpolluted area (cm)
Length measurements
polluted area (cm)
1 27 25
2 28 26
3 30 28
4 29 27
5 28 23
6 28 21
7 28 19
8 31 28
9 25 23
10 23 24
11 21 26
12 26 28
13 28 25
14 30 26
15 27 25
16 21
17 24