# MCQs: ANOVA & Hypothesis Testing

I need help answering these questions.

10) For a sample size of 1, the sampling distribution of the mean will be normally distributed

A.

Regardless of the shape of the population.

B.

Only if the population values are larger than 30.

C.

Only if the shape of the population is positively skewed.

D.

Only if the population is normally distributed.

11) The standard error of the sample mean is equal to 5 when n=25. If the sample size increases by a factor of four, who will the standard error change?

A.

It will double.

B.

It will be cut to ¼ of 5.

C.

It will be cut in half.

D.

It will quadruple.

12) A random variable follows the Student's t distribution. The probability that it will be positive is

A.

1

B.

Less than 0.50

C.

.05

D.

0

13) A test for equality of two variances is based on

A.

the difference between the sample coefficients of variation.

B.

the difference between the population variances.

C.

the ratio of the sample variances.

D.

the difference between the sample variances.

14) When testing for differences between two means, the Behrens-Fisher problem arises when the sample populations are

A.

are non-normal and have equal variances.

B.

are normal with unequal variances.

C.

are non-normal and have unequal variances.

D.

normal with equal variances.

15) A test for equality of two variances has sample sizes n1 = 13 and n2 = 10. The degrees of freedom for the test are

A.

13 and 10.

B.

26.

C.

12 and 9.

D.

21.

16) In two-factor ANOVA, the MSE must always be positive, but MSA or MSB may be negative.

A.

True

B.

False

17) Main effects are simpler to interpret when the test of the interaction term is not significant in a two-factor ANOVA.

A.

True

B.

False

18) An analysis of variance (ANOVA) tests population variance.

A.

True

B.

False

19) Hartley's test measures the equality of the means for several groups.

A.

True

B.

False

20) When the problem objective is to compare more than two populations, the experimental design that is the counterpart of the matched pairs experiment is called the randomized block design.

A.

True

B.

False

21) Which of the following statistics from the ANOVA table do not have an additive relationship?

A.

Mean squares

B.

Degrees of freedom

C.

It is not possible to tell.

D.

Sum of squares

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#### Solution Summary

The solution provides answers to multiple choice questions and true or false questions on ANOVA and hypothesis testing.

Statistics: 20 MCQ on ANOVA, correlation, hypothesis testing etc.

Question 1: For an experiment comparing more than two treatment conditions you should use analysis of variance rather than separate t tests because:

conducting several t tests would inflate the risk of a Type I error.

separate t tests would require substantially more computations .

a test based on variances is more sensitive than a test based on means.

There is no differences between the two tests, you can use either one.

Question 2: A negative value for a correlation indicates .

decreases in X tend to be accompanied by increases in Y

a much stronger relationship than if the correlation were positive

decreases in X tend to be accompanied by decreases in Y

a much weaker relationship than if the correlation were positive

Question 3: An analysis of variance comparing three treatment conditions produced dftotal = 24. For this ANOVA, what is the value of dfwithin?

21

3

22

2

Question 4: In general the distribution of F-ratios is .

positively skewed with all values greater than or equal to zero

negatively skewed with all values greater than or equal to zero

symmetrical with a mean of zero

symmetrical with a mean equal to dfbetween

Question 5 : A scatter-plot shows a set of data points that are widely scattered around a line that slopes up to the right. Which of the following values would be closest to the correlation for these data?

0.8

0.4

-0.8

-0.4

Question 6 : A set of n = 5 pairs of X and Y values has ΣX = 10, ΣY = 20, and ΣXY = 60. For this set of scores, the value of SP is .

-28

60

-20

20

Question 7 If the null hypothesis is true and there is no treatment effect, what value is expected on average for the F-ratio?

0

1

N - k

k - 1

Question 8: An analysis of variance is used to evaluate the mean differences for a research study comparing three treatments with a separate sample of n = 6 in each treatment. If the data produce an F-ratio of F = 4.10, then which of the following is the correct statistical decision?

Fail to reject the null hypothesis with either α = .05 or α = .01.

There is not enough information to make a statistical decision.

Reject the null hypothesis with either α = .05 or α = .01.

Reject the null hypothesis with α = .05 but not with α = .01.

Question 9: Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = -0.257, n = 90

Critical values: r = ±0.217, no significant linear correlation

Critical values: r = ±0.207, no significant linear correlation

Critical values: r = ±0.207, significant linear correlation

Critical values: r = 0.217, significant linear correlation

Question 10 : Which of the following is a characteristic of a correlational study?

participants are assigned to groups

participants are assigned to treatment conditions

participants are separated into groups based on a specific characteristic such as age or gender

none of the other options is a characteristic of a correlational study

Question 11: Which of the following pairs of variables should produce a correlation near 0?

driving distance from college and weekly cost of gas for a group of commuting college students

model year (2003, 2004, etc.) and price for a used Honda

IQ and weight for a group of third grade students

number of hours studying and number of errors on a math exam

Question 12: The purpose for post tests is .

to determine whether or not a Type I error was committed

to determine which treatments are significantly different

to determine how much difference exists between the treatments

None of these choices are correct.

Question 13: An analysis of variance comparing three treatment conditions produces dftotal = 24. For this ANOVA, what is the value of dfbetween?

2

21

3

22

Question 14: The Pearson correlation measures .

the degree of linear relationship.

the degree to which the relationship is consistently one directional.

the degree of the relationship without regard to the form of the relationship.

the degree of curvilinear relationship.

Question 15: Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = -0.695 , n = 25

Critical values: r = ±0.487, significant linear correlation

Critical values: r = ±0.396, significant linear correlation

Critical values: r = ±0.487, no significant linear correlation

Critical values: r = ±0.396, no significant linear correlation

Question 16: For an F-ratio with df = 2, 10, the critical value for a hypothesis test using α = .05 would be .

99.4

19.39

7.56

4.1

Question 17: Results of an analysis of variance produces SSbetween = 20, SSwithin = 30, and an F-ratio with df = 2, 15. For this analysis, what is the F-ratio?

20/30 = 0.67

10/2 = 5.00

30/20 = 1.50

2/10 = 0.20

Question 18: A set of n = 5 pairs of X and Y values has SSX = 5, SSY = 20, and SP = 8. For these data, the Pearson correlation is .

r = 8/20 = 0.40

r = 8/25 = 0.32

r = 8/100 = 0.08

r = 8/10 = 0.80

Question 19: A researcher reports an F-ratio with df = 3, 36 from an independent-measures research study. Based on the df values, how many treatments were compared in the study and what was the total number of subjects participating in the study?

2 treatments and 35 subjects

3 treatments and 37 subjects

4 treatments and 40 subjects

4 treatments and 36 subjects

Question 20: What is the value of SP for the following set of data?

X Y

1 5

3 3

5 1

8

19

0

-8

See the attached file.

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