For all hypothesis tests: Assume all samples are simple
random samples selected from normally distributed populations. If
testing means of two independent samples, assume variances are
unequal. For each test give the null and alternative hypothesis,
pvalue, and conclusion as it relates to the claim.
 In a random sample of 360 women, 65% favored stricter gun
control laws. In a random sample of 220 men, 60% favored stricter
gun control laws. Test the claim that the proportion of women
favoring stricter gun control is higher than the proportion of men
favoring stricter gun control. Use a significance level of
0.05.
Claim:
Hypothesis:
Test Run:
Pvalue:
Decision:
Conclusion:
 A researcher wishes to determine whether the blood pressure of
vegetarians is, on average, lower than the blood pressure of
nonvegetarians. 85 vegetarians were sample yielding a mean of 124.1
mmHg and a standard deviation of 38.7 mmHg. 75 nonvegetarians were
sampled yielding a mean of 138.7 mmHg and a standard deviation of
39.2 mmHg. Use a significance level of 0.01 to test the claim that
the mean systolic blood pressure of vegetarians is lower than the
mean systolic blood pressure of nonvegetarians.
Claim:
Hypothesis:
Test Run:
Pvalue:
Decision:
Conclusion:
 Students took a math test before and after tutoring. Their
scores, in points, are listed in the table below.
Subject

A

B

C

D

E

F

G

H

I

Before

71

66

75

70

66

53

72

78

62

After

75

75

73

82

78

72

85

90

75

 Using a 0.05 level of significance, test the claim that the
tutoring has a positive effect on the math scores.
Claim:
Hypothesis:
Test Run:
Pvalue:
Decision:
Conclusion:

 Based on your conclusion what would you tell a student who
asked if tutoring was worth the time and effort? Explain using the
test results.

 Create a confidence interval using the appropriate confidence
level in this case.

 Interpret this interval in terms of how much improvement a
student could see on average through tutoring.
 Many drivers of cars that can run on regular gas actually buy
premium in the belief that they will get better gas mileage. To
test that belief, we use 10 cars from a company fleet in which all
the cars run on regular gas. Each car is filled first with either
regular or premium gasoline, decided by a coin toss, and the
mileage for that tankful is recorded. Then the mileage is recorded
again for the same cars for a tankful of the other kind of
gasoline. We don’t let the drivers know about the experiment.

 Is there evidence that cars get significantly better fuel
economy with premium gas? Use α = 0.05
Claim:
Hypothesis:
Test Run:
Pvalue:
Decision:
Conclusion:

 How big might that difference be? Check with a confidence
interval using the appropriate level and include
interpretation

 Even if there is a significant difference, why might the
company choose to stick with regular gasoline? (Think in terms of
practical significance.)