# 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.

13.Which of the following is a research question that could be addressed using a one-way analysis of variance?

A) Are the proportions of people who oppose capital punishment different for three different age groups?

B) Is there a relationship between political party preference and age?

C) Does the variance of blood pressure differ for three different age groups?

D) Does mean blood pressure differ for three different age groups?

14.Which one of the following choices describes a problem for which an analysis of variance would be appropriate?

A) Comparing the proportion of successes for three different treatments of anxiety. Each treatment is tried on 100 patients.

B) Comparing the mean birth weights of newborn babies for three different racial groups.

C) Analyzing the relationship between high school GPA and college GPA.

D) Analyzing the relationship between gender and opinion about capital punishment (favor or oppose).

15.What procedure is used to test whether or not three or more population means are equal?

A) Analysis of correlation

B) Analysis of variance

C) Chi-square test

D) 3-sample t-test

16.A study compared grade point averages (GPA) among students in 4 different majors (English, History, Statistics, and Art) using analysis of variance. A total sample size of 20 students (5 in each major) was studied. The p-value for the F-test is 0.013. If the significance level, α, is 0.05, what is the conclusion from the analysis of variance?

A) The null hypothesis is not rejected; the population means are significantly different.

B) The null hypothesis is rejected; the population means are significantly different.

C) The null hypothesis is not rejected; the sample means are not significantly different.

D) The null hypothesis is not rejected; the population means are not significantly different.

E) The null hypothesis is rejected; the population means are not significantly different.

F) The null hypothesis is rejected; the sample means are not significantly different.

G) The null hypothesis is rejected; the sample means are significantly different.

H) The null hypothesis is not rejected; the sample means are significantly different.

17.On a survey conducted at a university, students were asked how they felt about their weight (about right, overweight, or underweight), and also were asked to record their grade point average (GPA). There were 235 responses, with 160 saying their weight was about right, 50 said they were overweight, and 17 underweight. The question of interest is whether mean GPA is the same or differs for different weight attitude populations. Minitab output for the study is given above. The p-value of 0.008 is found by calculating:

A) the area to the right of 4.98 under an F-distribution with 2 and 234 degrees of freedom.

B) the area to the right of 4.98 under an F-distribution with 2 and 232 degrees of freedom.

C) the area to the right of 4.98 under an F-distribution with 2 and 231 degrees of freedom.

18.When a one-way analysis of variance test is done, what probability distribution is used to find the p-value?

A) normal distribution

B) Chi-square distribution

C) t-distribution

D) F-distribution

19.Five different training programs for improving endurance are compared. Forty individuals are randomly divided into five groups of n = 8 each and a different training program is assigned to each group. After two months, the improvement in endurance is recorded for each participant. A one-way analysis of variance is used to compare the five training programs, and the resulting p-value is 0.023. At a significance level of 0.05, the appropriate conclusion about mean improvement in endurance is that it

A) is different for each of the five training programs

B) differs for at least two of the five training programs.

C) is significantly better for one of the training programs than for the other four.

D) is the same for the five training programs.

20.On a survey conducted at a university, students were asked how they felt about their weight (about right, overweight, or underweight), and also were asked to record their grade point average (GPA). There were 235 responses, with 160 saying their weight was about right, 50 said they were overweight, and 17 underweight. The question of interest is whether mean GPA is the same or differs for different weight attitude populations. Minitab output for the study is given above. The mean square error (MSE) in this study is:

A) 49.719

B) 2.134

C) 1.067

D) 0.214