# MATHEMATICS

1.A hypothesis test gives a p-value of 0.30. If the significance level α = 0.05, the results are said to be
A) practically significant because the p-value > α.
B) statistically significant because the p-value > α.
C) not practically significant because the p-value > α.
D) not statistically significant because the p-value > α.

2.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) A test of Ho: ρ = 0.3 versus Ha: ρ ≠ 0.3 would not be rejected using a = 0.05.
B) It is plausible that a majority 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) It is plausible that about 37% of all drivers would admit that they sometimes run red lights when no one is around.

3.The primary purpose of a significance test is to
A) estimate the p-value of a sample.
B) decide whether there is enough evidence to support a research hypothesis, Ha, about a population.
C) decide whether there is enough evidence to support a research hypothesis, Ha, about a sample.
D) estimate the p-value of a population.

4.The primary purpose of a significance test is to
A) decide whether there is enough evidence to support a research hypothesis, Ha, about a sample.
B) decide whether there is enough evidence to support a research hypothesis, Ha, about a population.
C) estimate the p-value of a sample.
D) estimate the p-value of a population.

5.The p-value for a one-sided test for a mean was 0.04. The p-value for the corresponding two-sided test would be:
A) 0.04
B) 0.02
C) 0.08
D) 0.06

6.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

7.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). What is the appropriate alternative hypothesis for this question?
A) x-bar1 − x-bar2 ≠ 0
B) μ1 − μ2 < 0
C) μ1 − μ2 = 0
D) x-bar1 − x-bar2 < 0

8.A shopper wanted to test whether there was a difference in the average waiting times at the check-out counter among 5 different supermarkets. She selected a random sample of 20 shoppers from each of the five supermarkets. What is the alternative hypothesis for this situation?
A) The average waiting time to check out is 25 minutes for all five supermarkets.
B) The average waiting time to check out is the same for all five supermarkets.
C) The average waiting time to check out is not the same for all five supermarkets.
D) The average waiting time for each of the 100 shoppers is different.

9.Ninety people with high cholesterol are randomly divided into three groups of thirty, and a different treatment program for decreasing cholesterol is assigned to each group. The response variable is the change in cholesterol level after two months of treatment. An analysis of variance will be used to compare the three treatments. What null hypothesis is tested by this ANOVA F-test?
A) The sample means are equal for the three treatment groups.
B) The sample variances are equal for the three treatment groups.
C) The population means are equal for the three treatments
D) The population variances are equal for the three treatments.

10.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. What are the numerator and denominator degrees of freedom for the ANOVA F-test?
A) 5 for numerator and 20 for denominator.
B) 3 for numerator and 16 for denominator.
C) 4 for numerator and 79 for denominator.

11.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 231 degrees of freedom.
C) the area to the right of 4.98 under an F-distribution with 2 and 232 degrees of freedom.

12.A study compared testosterone levels among athletes in four sports: soccer, track, Lacrosse, and water polo. The total sample size was n =30 (10 soccer, 10 track, 5 Lacrosse, and 5 water polo). A one-way analysis of variance was used to compare the population mean levels for the four sports. The sum of squared errors is SS Error = 100. What is the value of the Mean Square Error (MS Error)?
A) 3.45
B) 3.85
C) 10

13.Which of the following variables COULD be used in a Chi-Square analysis?
A) All of the above
B) Gender
C) Race
D) Age
E) Political Party Affiliation
F) Course Section Number

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