1 An F-test can also be used to compare the variances of three or more means.
2) If the null hypothesis is not rejected, it can be assumed the proportions are __________ and the differences in them are due to chance
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?
Sample size 50 80
Mean effect 7 6.95
Sample variance 3 4
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?
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)
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
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.
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
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
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.