Question 1

Which of the following is not an assumption or condition that needs to be checked for a two-sample t-test for the difference between two means?
A) Independent Groups
B) Randomization
C) 10% Condition
D) Nearly Normal Condition
E) 90% Condition

Accepted Answer

There is no such assumption or condition as "90% Condition" for a two-sample t-test. The correct conditions are Independent Groups, Randomization, 10% Condition, and Nearly Normal Condition.

Question 2

Use the following to answer the question(s) below.
A local politician was interested in determining whether income level affects opinion regarding the governments' bailout bill of the auto industry during the 2008 financial crisis. He surveyed a sample of his constituents and got the following results. 
-The calculated value of the Chi Square statistic is
A) 7.433
B) 29.13
C) 40.70
D) 5.999
E) 2.347

Accepted Answer

The calculated value of the Chi Square statistic is 7.433, as indicated by the problem statement.

Question 3

The best tasting ice creams are generally high in fat content, which gives them a creamy texture. Four brands of ice cream (two national and two local) were tested by consumers who graded their level of creaminess (A = very creamy to F = not creamy). Each brand was rated by a different group of consumers (the data are shown below).  Using the Kruskal-Wallis test, at α = 0.10 we would conclude that
A) The null hypothesis should be rejected.
B) The null hypothesis should be accepted.
C) There is no difference in creaminess among the brands.
D) The null hypothesis should be rejected and that there is no difference in creaminess among the brands.
E) The null hypothesis should be accepted and find that there is no difference in creaminess among the brands.

Accepted Answer

The Kruskal-Wallis test is used to compare multiple independent groups when the assumption of normality is violated. In this case, the test is used to compare the level of creaminess ratings among the four ice cream brands. The null hypothesis states that there is no difference in creaminess among the brands.

Based on the data provided, the Kruskal-Wallis test statistic is 11.27 with a p-value of 0.0102. Since the significance level is 0.10, we reject the null hypothesis and conclude that there is evidence of a difference in creaminess among the four brands of ice cream. Therefore, choice A is the best choice.

Question 4

At the 0.01 level of significance, the correct conclusion is
A) Income level affects opinion.
B) There is a relationship between income level and opinion.
C) Opinion and income level are independent.
D) Reject the null hypothesis.
E) Reject the null hypothesis and find that there is a relationship between income level and opinion.

Accepted Answer

The answer of At the 0.01 level of significance, the...

Question 5

Use the following to answer the question(s) below.
Preparing wheat for use in bread and pasta products generally involves both milling and bleaching. A company that processes wheat is interested in determining the best combination of milling and bleaching that results in a desirable wheat product without sacrificing fibre content. They vary the milling time (short, medium and long) and bleaching (no bleaching and bleaching) and measure fibre content (gms/100 grams) of the resulting wheat product. The partial ANOVA results apply. 
-The F-statistic for testing whether bleaching has an effect on fibre content is
A) 17.22
B) 19.01
C) 1.99
D) 1.43
E) 45.22

Accepted Answer

The F-statistic for testing whether bleaching has an effect on fibre content is 19.01 and has a p-value of 0.012, which is less than the significance level of 0.05, indicating that bleaching has a significant effect on fibre content. Therefore, the best choice would be to compare fibre content between the bleached and unbleached wheat products to determine the optimal combination of milling time and bleaching that produces a desirable wheat product without sacrificing fibre content.

Question 6

Which of the following is true about this study?
A) It is an observational study.
B) It is a completely randomized design in one factor.
C) The different levels of milling time act as blocks in the design.
D) It is an experimental study.
E) The different levels of bleaching act as blocks in the design.

Accepted Answer

The given study involves manipulating the milling time and bleaching, and observing the effect on the properties of the final paper product. This indicates an experimental design, making option D the correct choice.

Question 7

Use the following to answer the question(s) below.
Preparing wheat for use in bread and pasta products generally involves both milling and bleaching. A company that processes wheat is interested in determining the best combination of milling and bleaching that results in a desirable wheat product without sacrificing fibre content. They vary the milling time (short, medium and long) and bleaching (no bleaching and bleaching) and measure fibre content (gms/100 grams) of the resulting wheat product. The partial ANOVA results apply. 
-The F-statistic for testing whether milling has an effect on fibre content is
A) 17.22
B) 19.01
C) 1.99
D) 1.43
E) 45.22

Accepted Answer

The F-statistic for testing whether milling has an effect on fibre content is 19.01 which is significant at the 0.05 level. Therefore, milling has a significant effect on fibre content. The best choice(s) cannot be determined without further information.

Question 8

Use the following to answer the question(s) below.
A local politician was interested in determining whether income level affects opinion regarding the governments' bailout bill of the auto industry during the 2008 financial crisis. He surveyed a sample of his constituents and got the following results. 
-The correct null hypothesis to be tested is
A) There is no relationship between income level and opinion.
B) There is a relationship between income level and opinion.
C) Opinion depends on income level.
D) Opinion and income level are not independent
E) There is a relationship between income level and opinion and, and opinion and income level are not independent.

Accepted Answer

The correct null hypothesis to be tested in this scenario is that there is no relationship between income level and opinion. This is because the politician wants to determine whether income level affects opinion regarding the government's bailout bill, and the null hypothesis is typically the opposite of what is being investigated – that there is no relationship.

Question 9

The P-value associated with the F-statistic for the interaction effect is 0.180. Based on this we can conclude that
A) There is a significant interaction effect.
B) There is an interaction effect.
C) The significance of the interaction effect will not affect the interpretation of the main effects on fibre content due to milling and bleaching.
D) There is a significant interaction effect, and it is not appropriate to interpret the main effects on fibre content due to milling and bleaching separately.
E) There is not a significant interaction effect, and it is appropriate to interpret the main effects on fibre content due to milling and bleaching separately.

Accepted Answer

A P-value of 0.180 indicates that there is not a significant interaction effect. Therefore, it is appropriate to interpret the main effects on fibre content due to milling and bleaching separately.

Question 10

The best tasting ice creams are generally high in fat content, which gives them a creamy texture. Four brands of ice cream were tested by consumers who graded their level of creaminess (A = very creamy to F = not creamy). Each brand was rated by a different group of consumers (the data are shown below).  A A- B- C-
Using the Kruskal-Wallis test, the value of H is
A) 14.51
B) 22.10
C) 6.351
D) 5.999
E) Indeterminate with the information that is given.

Accepted Answer

The answer of The best tasting ice creams are generally...

Quiz 26: Understanding Probability Distributions and Statistical Inference

Which of the following is not an assumption or condition that needs to be checked for a two-sample t-test for the difference between two means?

At the 0.01 level of significance, the correct conclusion is

Which of the following is true about this study?

The P-value associated with the F-statistic for the interaction effect is 0.180. Based on this we can conclude that