# MATHEMATICS

1.The data summary used to calculate the p-value in order to decide between the null hypothesis and the alternative hypothesis is called a

A) test statistic.

B) statistically significant result.

C) significance level.

D) p-value.

2. Determine if the statement is a typical null hypothesis (Ho) or alternative hypothesis (Ha). The average price of a particular statistics textbook over the internet is the same as the average price of the textbook sold at all bookstores in a college town.

A) Alternative hypothesis

B) Null hypothesis

3. Suppose a 95% confidence interval for p, the proportion of drivers who admit that they sometimes run red lights when no one is around, is 0.29 to 0.38. Which of the following statements is false?

A) It is plausible that a majority of all drivers would admit that they sometimes run red lights when no one is around.

B) It is plausible that about 37% of all drivers would admit that they sometimes run red lights when no one is around.

C) A test of Ho: ρ = 0.5 versus Ha: ρ ≠ 0.5 would be rejected using a = 0.05.

D) A test of Ho: ρ = 0.3 versus Ha: ρ ≠ 0.3 would not be rejected using a = 0.05.

4. A hypothesis test for a population proportion ρ is given below:

Ho: ρ = 0.10 Ha: ρ ≠ 0.10

If the sample size n = 500 and sample proportion ρ-hat = 0.04, then the z-statistic is:

A) -4.47

B) 6.84

C) -6.84

D) 4.47

5.Which of the following is not one of the steps for hypothesis testing?

A) Assuming the null hypothesis is true, find the p-value.

B) Verify data conditions and calculate a test statistic.

C) Determine the null and alternative hypotheses.

D) Assuming the alternative hypothesis is true, find the p-value.

6.A null hypothesis is that the average pulse rate of adults is 70. For a sample of 64 adults, the average pulse rate is 71.8. A significance test is done and the p-value is 0.02. What is the most appropriate conclusion based on α of 0.05?

A) Reject the hypothesis that the population average pulse rate is 70.

B) Conclude that the population average pulse rate is 71.8.

C) Reject the hypothesis that the sample average pulse rate is 70.

D) Conclude that the population average pulse rate is 70.

7.It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left – right) was found. The alternative hypothesis is one-sided (left hand stronger). The resulting t-statistic was 1.90. This is an example of

A) an unpooled t-test.

B) a two-sample t-test.

C) a paired t-test.

D) a pooled t-test.

8. Which of the following is not one of the steps for hypothesis testing?

A) Assuming the null hypothesis is true, find the p-value.

B) Verify data conditions and calculate a test statistic.

C) Determine the null and alternative hypotheses.

D) Assuming the alternative hypothesis is true, find the p-value.

9. It is known that for right-handed people, the dominant (right) hand tends to be stronger. For left-handed people who live in a world designed for right-handed people, the same may not be true. To test this, muscle strength was measured on the right and left hands of a random sample of 15 left-handed men and the difference (left – right) was found. The alternative hypothesis is one-sided (left hand stronger). The resulting t-statistic was 1.90. Assuming the conditions are met, based on the t-statistic of 1.90 the appropriate conclusion for this test using α = 0.05 and using T-Table is

A) The results are statistically significant so the left hand does not appear to be stronger.

B) The results are not statistically significant so there is not enough evidence to conclude the left hand appears to be stronger.

C) The results are statistically significant so the left hand appears to be stronger.

10. A null hypothesis is that the mean nose lengths of men and women are the same. The alternative hypothesis is that men have a longer mean nose length than women. Which of the following is the correct way to state the null hypothesis?

A) ρ = 0.5

B) μ1 − μ2 = 0

C) x-bar1 − x-bar2 = 0

D) ρ1 − ρ2 = 0

11. A researcher wants to assess if there is a difference in the average age of onset of a certain disease for men and women who get the disease. Let μ1 = average age of onset for women and μ2 = average age of onset for men. A random sample of 30 women with the disease showed an average age of onset of 83 years, with a sample standard deviation of 11.5 years. A random sample of 20 men with the disease showed an average age of onset of 77 years, with a sample standard deviation of 4.5 years. Assume that ages at onset of this disease are normally distributed for each gender, do not assume the population variances are equal. What are the appropriate null and alternative hypotheses?

A) μ1 ≠ μ2 and Ha: μ1 = μ2

B) μ1 = μ2 and Ha: μ1 > μ2

C) μ1 = μ2 and Ha: μ1 < μ2

D) μ1 = μ2 and Ha: μ1 ≠ μ2

12.In the survey of a random sample of students at a university, two questions were “How many hours per week do you usually study?” and “Have you smoked marijuana in the past six months?” An analysis of the results produced the above Minitab output. A research question of interest is whether students who have smoked marijuana (group 1) in the past 6 months study fewer hours on average per week than those who have not (group 2). Based on the information given in the output, what conclusion can be made about the difference in time spent studying for the two groups?

A) There is not a statistically significant difference.

B) It is impossible to know if there is a statistically significant difference because the test is one-sided and the information provided is two-sided.

C) There is a statistically significant difference.

D) It is impossible to know if there is a statistically significant difference because no p-value is provided.