Question

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, p-value, and conclusion as it relates to the claim.

1. 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:

P-value:

Decision:

Conclusion:

2. 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:

P-value:

Decision:

Conclusion:

3. 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

1. 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:

P-value:

Decision:

Conclusion:

1. 2. 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.
2. 3. Create a confidence interval using the appropriate confidence level in this case.
3. 4. Interpret this interval in terms of how much improvement a student could see on average through tutoring.
4. 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.
5. 1. Is there evidence that cars get significantly better fuel economy with premium gas? Use α = 0.05

Claim:

Hypothesis:

Test Run:

P-value:

Decision:

Conclusion:

1. 2. How big might that difference be? Check with a confidence interval using the appropriate level and include interpretation
2. 3. Even if there is a significant difference, why might the company choose to stick with regular gasoline? (Think in terms of practical significance.)

Answer 1