# MATHEMATICS

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.

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

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