# Statistics

1 An F-test can also be used to compare the variances of three or more means.

True

False

2) If the null hypothesis is not rejected, it can be assumed the proportions are __________ and the differences in them are due to chance

a) Equal

b) Unequal

c) Small

d) Large

3) A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and for men. At a= .05, what is the test value?

Woman Men

Sample size 50 80

Mean effect 7 6.95

Sample variance 3 4

a) 0.45

b) 0.33

c) 6.63

d) 0.15

4) For the samples summarized below, test the hypothesis at alpha =.05 that the two variances are equal.

Variance Number of data values

Sample1 25 9

Sample2 9 19

a) Do not reject the hypothesis because the test value 7.72 is greater than the critical value 3.01.

b) Reject the hypothesis because the test value 2.78 is less than the critical value 2.88.

c) Reject the hypothesis because the test value 7.72 is greater than the critical value 2.88.

d) Do not reject the hypothesis because the test value 2.78 is less than the critical value 3.01.

5) A random group of students was selected from a large student conference to analyze their class in school. Is there evidence to reject the hypothesis that the number of students is equally distributed between the four classes, at alpha = .05?

Freshman sophmore junior senior

Number of students 9 9 13 21

a) There is evidence to reject the claim that students are equally distributed between the four classes because the test value 7.815 > 7.385

b) There is not evidence to reject the claim that the customers' preferences are distributed between the four classes because the test value 7.385 < 9.488

c) There is evidence to reject the claim that students are equally distributed between the four classes because the test value 9.488 > 7.385

d) There is not evidence to reject the claim that students are equally distributed between the four classes because the test value 7.385 < 7.815

6) If there are 3 means to be compared, then how many possible different comparisons are there altogether?

A) 4

B) 3

C) 6

D) 9

7) A marketing firm asked a random set of married and single men as to how much they were willing to spend for a vacation. At alpha = 0.05, is a difference in the two amounts?

Married men Single men

Sample size 50 50

Mean spending 380 325

Sample variance 6000 9000

a) No, because the test value 0.18 is inside the interval (-1.96, 1.96)

b) Yes, because the test value 3.18 is outside the interval (-1.96, 1.96)

c) Yes, because the test value 1.50 is inside the interval (-1.96, 1.96)

d) No, because the test value 1.50 is outside the interval (-1.96, 1.96)

8) In an Analysis of Variance Summary Table, if the Mean Square Between = 35 and the Mean Square Within = 28, then the null hypothesis of the groups having the same mean is

a) There is not evidence to reject the claim because 35 > 28

b) There is evidence to reject the claim because 35 > 28

c) Cannot be determined without knowing the Sums of Squares (between and within)

d) Cannot be determined without knowing the Degrees of Freedom (between and within)

9) An anatomy teacher hypothesizes that the final grades in her class are distributed as 10% A's, 23% B's, 45% C's, 14% D's, and 8% F's. What is the critical value if at the end of the semester she has the following grades? Use a=0.05.

a b c d f

6 14 22 8 4

a) 9.236

b) 7.779

c) 11.070

d) 9.488

10) If the test value in the figure below, for a test of the difference between two large sample means, is 2.57 when the critical value is 1.96, what decision about the hypothesis should be made?

a) reject the null hypothesis

b) do not reject the null hypothesis

c) reject the alternative hypothesis

d) not enough information

11) A researcher wanted to investigate whether there is a significant difference in the average age of instructors, assistant professors, associate professors, and full professors at a university.

The faculty was selected at random and their ages were recorded. Use the collected data to complete the ANOVA chart given below.

Raw data

Instructors assistant professors associate professors professors

26 28 45 58

32 32 48 56

29 36 52 62

36 45 54 65

40 50 62 52

45 46 65 49

Anova summary

Source of variation sum of squares degrees of freedom variation f value f critical

Between groups 3 12.88 3.10

Within groups 1120.17

Total 3283.63 23

12) Use the given contingency table to (a) find the expected frequencies of each cell in the table, (b) perform a chi-square test for independence, and (c) comment on the relationship between the two variables. Assume the variables are independent

The contingency table shows the results of a random sample of 500 individuals classified by gender and type of vehicle owned. Use α = 0.01.

Type of vehicle owned

Gender car truck suv van

Male 90 100 50 7

Female 110 75 65 3

#### Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Statistics and provides students with a clear perspective of the underlying concepts.