A+ Answers





A hypothesis test produces a t statistic of t = 2.20.  If the researcher is using a two-tailed test with  = .05, how large does the sample have to be in order to reject the null hypothesis?

Select one:

 a. At least n = 13

 b. At least n = 14

 c. At least n = 11

 d. At least n = 12

Question 2

A repeated-measures study comparing two treatments with a sample of n = 4 participants produces a mean of M = 18 with SS = 24 for the scores in the first treatment, a mean of M = 14 with SS = 18 for the scores in the second treatment, and a mean of M = 4 with SS = 12 for the difference scores.  What is the estimated standard error for the sample mean difference?

Select one:

 a. 3

 b. 2

 c. 4

 d. 1

Question 3

A research report describing the results from a repeated-measures study states: The data show no significant difference between the two treatments, t(10) = 1.65, p > .05.  Based on this report, you can conclude that a total of ____ individuals participated in the research study .

Select one:

 a. 9

 b. 11

 c. 10

 d. 12

Question 4

A researcher administers a treatment to a sample of participants selected from a population with µ = 80.  If the researcher obtains a sample mean of M = 88, which combination of factors is most likely to result in rejecting the null hypothesis?

Select one:

 a.  = 10 and n = 50

 b.  = 10 and n = 25

 c.  = 5 and n = 25

 d.  = 5 and n = 50

Question 5

A researcher conducts a hypothesis test using a sample of n = 40 from an unknown population.  What is the df value for the t statistic?

Select one:

 a. It cannot be determined from the information given.

 b. 40

 c. 39

 d. 41

Question 6

A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population which is known to have a mean of  = 80.  The results will be examined using a one-tailed hypothesis test.  Which of the following is the correct statement of the null hypothesis?

Select one:

 a.  < 80

 b.  > 80

 c.  < 80

 d.  > 80

Question 7

A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population.  If the researcher uses a one-tailed test with  = .01, then which of the following correctly identifies the critical region?

Select one:

 a. z > 2.58

 b. z > 2.33

 c. z < 2.58

 d. z < 2.33

Question 8

A researcher is using a repeated-measures study to evaluate the difference between two treatments.  If the difference between the treatments is consistent from one participant to another, then the data should produce ____.

Select one:

 a. a small variance for the difference scores and a small standard error

 b. a large variance for the difference scores and a small standard error

 c. a small variance for the difference scores and a large standard error

 d. a large variance for the difference scores and a large standard error

Question 9

A researcher uses a repeated-measures study to compare two treatment conditions with a set of 20 scores in each treatment.  What would be the value of df for the repeated-measures t statistic?

Select one:

 a. df = 19

 b. df = 38

 c. df = 39

 d. df = 18

Question 10

A sample of n = 16 scores produces a t statistic of t = 2.00.  If the sample is used to measure effect size with r2, what value will be obtained for r2?

Select one:

 a. r2 = 4/20

 b. r2  = 2/20

 c. r2 = 4/19

 d. r2  = 2/19

Question 11

A sample of n = 25 scores has a mean of M = 40 and a variance of s2 = 100.  What is the estimated standard error for the sample mean?

Select one:

 a. 1

 b. 2

 c. 4

 d. 

Question 12

A sample of n = 4 scores is selected from a population with an unknown mean.  The sample has a mean of M = 40 and a variance of s2 = 16.  Which of the following is the correct 90% confidence interval for ?

Select one:

 a.  = 40 ± 2.353(2)

 b.  = 40 ± 1.638(2)

 c.  = 40 ± 2.353(4)

 d.  = 40 ± 1.638(4)

Question 13

A treatment is administered to a sample of n = 9 individuals selected from a population with a mean of  = 80 and a standard deviation of  = 12.  After treatment, the effect size is measured by computing Cohen’s d, and a value of d = 0.50 is obtained.  Based on this information, what is the mean for the treated sample?

Select one:

 a. M = 82

 b. M = 86

 c. M = 6

 d. This cannot be answered without knowing the sample size.

Question 14

An analysis of variance produces SSbetween = 30, SSwithin = 60, and an F-ratio with df = 2, 15.  For this analysis, what is the F-ratio?

Select one:

 a. 15/4 = 3.75

 b. 30/60 = 0.50

 c. 60/30 = 2.00

 d. 4/15 = 0.27

Question 15

An analysis of variances produces dftotal = 29 and dfwithin = 27.  For this analysis, what is dfbetween?

Select one:

 a. This cannot be determined without additional information.

 b. 1

 c. 3

 d. 2

Question 16

An independent-measures study comparing two treatment conditions produces a t statistic with df = 18.  If the two samples are the same size, how many participants were in each of the samples?

Select one:

 a. 19

 b. 10

 c. 9

 d. 20

Question 17

An independent-measures study has one sample with n = 10 and a second sample with n = 15 to compare two experimental treatments.  What is the df value for the t statistic for this study?

Select one:

 a. 23

 b. 26

 c. 27

 d. 24

Question 18

An independent-measures study produces sample means of M1 = 35 and M2 = 31 and a pooled variance of 25.  For this study, Cohen’s d = ____.

Select one:

 a. d = 4/5

 b. d = 4/25

 c. d = 5/4

 d. d = 25/4

Question 19

Even if a treatment has an effect, it is still possible to obtain a sample mean that is very similar to the original population mean.  What outcome is likely if this happens?

Select one:

 a. Correctly reject H0.

 b. Correctly fail to reject H0.

 c. Fail to reject H0 and make a Type II error.

 d. Reject H0 and make a Type I error.

Question 20

For a repeated-measures study comparing two treatment conditions, a researcher obtains Cohen’s d = 0.50 for a sample of n = 4 scores with a variance of s2 = 16.  What is the value of the sample mean?

Select one:

 a. MD = 4

 b. MD = 16

 c. MD = 2

 d. MD = 8

Question 21

For an independent-measures research study, the data show an 8-point difference between the two treatment means and a pooled variance of 4.  Given this information, what is the value of Cohen’s d?

Select one:

 a. 8/2

 b. 8/4

 c. 4/8

 d. This cannot be answered without knowing the sample sizes.

Question 22

For which of the following situations would a repeated-measures research design be appropriate?

Select one:

 a. Comparing pain tolerance with and without acupuncture needles

 b. Comparing verbal solving skills for science majors versus art majors at a college

 c. Comparing mathematical skills for girls versus boys at age 10

 d. Comparing self-esteem for students who participate in school athletics versus those who do not

Question 23

How does sample variance influence the likelihood of rejecting the null hypothesis and measures of effect size such as r2 and Cohen’s d?

Select one:

 a. Larger variance decreases the likelihood but increases measures of effect size.

 b. Larger variance increases the likelihood but decreases measures of effect size.

 c. Larger variance decreases both the likelihood and measures of effect size.

 d. Larger variance increases both the likelihood and measures of effect size.

Question 24

If a researcher is using a t statistic to test a null hypothesis about a population, what information is needed from the population to calculate the t statistic?

Select one:

 a. You must know the population mean

 b. The t statistic does not require any information about the population

 c. You must know the population mean and the variance or standard deviation

 d. You must know the population variance or standard deviation

Question 25

If a sample of n = 16 scores is being used to make an 80% confidence interval estimate of the population mean, , what value(s) of t should be used?

Select one:

 a. t = ±1.753

 b. t = ±2.131

 c. t = 0

 d. t = ±1.341

Question 26

If an analysis of variance is used for the following data, what would be the effect of changing the value of M2 to 20?

Sample Data

M1 = 10    M2 = 15

SS1 = 90    SS2 = 70

Select one:

 a. Decrease SSbetween and increase the size of the F-ratio.

 b. Increase SSbetween and decrease the size of the F-ratio.

 c. Decrease SSbetween and decrease the size of the F-ratio.

 d. Increase SSbetween and increase the size of the F-ratio.

Question 27

If other factors are held constant, which of the following sets of data would produce the largest value for an independent-measures t statistic?

Select one:

 a. The two samples both have n = 30 with sample variances of 20 and 25.

 b. The two samples both have n = 15 with sample variances of 20 and 25.

 c. The two samples both have n = 15 with variances of 120 and 125.

 d. The two samples both have n = 30 with variances of 120 and 125.

Question 28

If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that  = 80?

Select one:

 a. M = 85 for a sample of n = 25

 b. M = 85 for a sample of n = 100

 c. M = 90 for a sample of n = 100

 d. M = 90 for a sample of n = 25

Question 29

If the sample mean difference is 3 points, which of the following sets of data would produce the largest value for Cohen’s d?

Select one:

 a. Cohen’s d is the same for all three of the samples.

 b. n = 20 for both samples and a pooled variance of 15

 c. n = 10 for both samples and a pooled variance of 15

 d. n = 30 for both samples and a pooled variance of 15

Question 30

In an analysis of variance, which of the following is determined the size of the sample variances?

Select one:

 a. SSbetween

 b. dfbetween

 c. SSwithin

 d. dfwithin

Question 31

In general, if the variance of the difference scores increases, then what will happen to the value of the t statistic?

Select one:

 a. It may increase or may decrease. There is no consistent relationship between variance and the size of the t statistic.

 b. It will stay the same; the t statistic is not affected by the variance of the difference scores.

 c. It will decrease (move toward 0 at the center of the distribution).

 d. It will increase (move farther toward the tail of the distribution).

Question 32

In general, what is the effect of an increase in the variance for the sample of difference scores?

Select one:

 a. A decrease in the standard error and an increase in the value of t

 b. A decrease in the standard error and a decrease in the value of t

 c. An increase in the standard error and an increase in the value of t

 d. An increase in the standard error and a decrease in the value of t

Question 33

Increasing the alpha level (for example from  = .01 to  = .05) ____.

Select one:

 a. increases the size of the critical region

 b. increases the probability that the sample will fall into the critical region

 c. increases the probability of a Type I error

 d. All of the other options are results of increasing alpha.

Question 34

One sample has a variance of s2 = 10 and a second sample has a variance of s2 = 6.  If the two samples have the same number of scores, what is the pooled variance for the two samples?

Select one:

 a. This cannot be answered without knowing the sample size.

 b. 4

 c. 14

 d. 8

Question 35

One sample has M = 18 and a second sample has M = 14.  If the pooled variance for the two samples is 16, then what is the value of Cohen’s d?

Select one:

 a. 1.00

 b. 0.25

 c. This cannot be determined with the information given.

 d. 0.50

Question 36

The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 16.  If there are n = 8 scores in each sample, then what is the estimated standard error for the sample mean difference?

Select one:

 a. 128

 b. 2

 c. 16

 d. 4

Question 37

The following data were obtained from a repeated-measures research study.  What is the value of MD for these data?

Subject   1st    2nd

#1           10      15

#2             4        8

#3            7         5

#4            6       11

Select one:

 a. 4.5

 b. 4

 c. 3.5

 d. 3

Question 38

The following table shows the results of an analysis of variance comparing two treatment conditions with a sample of n = 11 participants in each treatment.  Note that several values are missing in the table.  What is the missing value for the F-ratio?

Source         SS      df      MS     

Between      xx      xx      14      F = xx

Within         xx      xx      xx

Total           154     xx      

Select one:

 a. 28

 b. 7

 c. 2

 d. 14

Question 39

Two samples from the same population both have n = 10 scores with M = 45.  If the t statistic is computed for each sample, then what is the relationship between the two t values?

Select one:

 a. The two t statistics will be identical.

 b. The sample with the larger variance will produce the larger t statistic.

 c. There is no way to predict the relationship between the two t statistics

 d. The sample with the smaller variance will produce the larger t statistic.

Question 40

Two samples, each with n = 8, produce an independent-measures t statistic of t = -2.15.  Which of the following decisions is justified?

Select one:

 a. Reject H0 with  = .05 but fail to reject with  = .01.

 b. Fail to reject H0 with  = .05 but reject H0 with  = .01.

 c. Fail to reject H0 with  = .05 and fail to reject with  = .01.

 d. Reject H0 with  = .05 and reject H0 with  = .01.

Question 41

What is the purpose for post tests?

Select one:

 a. To determine how much difference exists between the treatments

 b. To determine which treatments are significantly different

 c. None of the above

 d. To determine whether or not a Type I error was committed

Question 42

What is the sample variance and the estimated standard error for a sample of  n = 9 scores with SS = 72?

Select one:

 a. s2 = 3 and sM = 3

 b. s2 = 9 and sM = 3

 c. s2 = 9 and sM = 1

 d. s2 = 3 and sM = 1

Question 43

When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests?

Select one:

 a. Using several t tests increases the risk of a Type II error.

 b. The analysis of variance is more likely to detect a treatment effect.

 c. Using several t tests increases the risk of a Type I error.

 d. There is no advantage to using an analysis of variance instead of several t tests.

Question 44

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?

Select one:

 a. It is flatter and more spread out than the normal distribution.

 b. It is almost perfectly normal.

 c. It is taller and narrower than the normal distribution.

 d. There is no consistent relationship between the t distribution and the normal distribution.

Question 45

Which combination of factors will increase the chances of rejecting the null hypothesis?

Select one:

 a. A small standard error and a large alpha level

 b. A large standard error and a small alpha level

 c. A large standard error and a large alpha level

 d. A small standard error and a small alpha level

Question 46

Which of the following accurately describes the effect of increasing the alpha level?

Select one:

 a. Increases the risk of a Type I error and has no effect on the standard error

 b. Decreases the risk of a Type I error and has no effect on the standard error

 c. Decreases the standard error and has no effect on the risk of a Type I error

 d. Increases the standard error and has no effect on the risk of a Type I error

Question 47

Which of the following is a fundamental difference between the t statistic and a z-score?

Select one:

 a. The t statistic uses the sample mean in place of the population mean.

 b. The t statistic computes the standard error by dividing the standard deviation by n – 1 instead of dividing by n.

 c. All of the above are differences between t and z.

 d. The t statistic uses the sample variance in place of the population variance.

Question 48

Which of the following is an accurate definition for the power of a statistical test?

Select one:

 a. The probability of rejecting a false null hypothesis

 b. The probability of supporting a false null hypothesis

 c. The probability of supporting true null hypothesis

 d. The probability of rejecting a true null hypothesis

Question 49

Which of the following is an accurate definition of a Type I error?

Select one:

 a. Rejecting a true null hypothesis

 b. Failing to reject a true null hypothesis

 c. Failing to reject a false null hypothesis

 d. Rejecting a false null hypothesis

Question 50

With  = .01 the two-tailed critical region for a t test using a sample of n = 16 subjects would have boundaries of ____.

Select one:

 a. t = ±2.947

 b. t = ±2.583

 c. t = ±2.602

 d. t = ±2.921