Question 1

A researcher conducts a study in which the same participants are observed across each level of the independent variable.If there are only two levels of the independent variable,then what type of t test is appropriate for this study?

Accepted Answer

A related-samples t test, also known as a paired-samples t test, is appropriate when the same participants are observed in each level of the independent variable. This type of test compares the means of two related groups to determine if there is a statistically significant difference between them. Since this study only has two levels of the independent variable, a related-samples t test is the most appropriate choice.

Question 2

A researcher selects a sample of 36 dog owners and measures their responsiveness to pictures depicting the humane and inhumane treatment of dogs.The researcher finds that responsiveness significantly differed,t = 3.243.Use $\eta$² to compute the proportion of variance for this result.

Accepted Answer

$\eta$² = .23 is the proportion of variance for this result because it is calculated by dividing the variance between groups by the total variance. In this case, the variance between groups is 3.243^2 = 10.51 and the total variance is 10.51 + 36 = 46.51. Therefore, $\eta$² = 10.51 / 46.51 = .23.

Question 3

A researcher conducts a study in which different participants are independently observed within groups,and the same participants are observed between groups.If there are only two groups,then what type of t test is appropriate for this study?

Accepted Answer

The study involves the same participants being observed within and between groups, which indicates a related-samples design. Therefore, a related-samples t test would be the best choice.

Question 4

Each of the following is needed to compute the estimated Cohen's d,except

Accepted Answer

To compute the estimated Cohen's d, we need the mean difference and the standard deviation of difference scores. The standard error is not necessary as it reflects the variability of sample means and not the variability of the observed data.

Question 5

A professor compares scores on a competency exam among students at two times during a single semester.What type of t test is most appropriate for this study?

Accepted Answer

A related-samples t test (also known as a paired-samples or dependent-samples t test) is appropriate for comparing scores on the same group of students at two different points in time during the same semester. This type of test is used to analyze the differences between two sets of scores that are dependent on each other.

Question 6

A researcher tests how well participants know their spouse while under hypnosis,and again without hypnosis.It was hypothesized that participant responses would be more accurate (greater number of correct responses)when under hypnosis.The mean number of correct responses was M = 5.30 under hypnosis and M = 3.40 without hypnosis in a sample of 30 participants.If the estimated standard error for difference scores was 2.52,then what is the decision at a .05 level of significance (two-tailed test)?

Accepted Answer

The mean difference is 5.30 - 3.40 = 1.90. The t-value is 1.90 / 2.52 = 0.754. The critical t-value for a two-tailed test with 29 degrees of freedom and a .05 level of significance is 2.045. Since the t-value is less than the critical t-value, we fail to reject the null hypothesis.

Question 7

All other things being equal,as the degrees of freedom increase,what happens to the critical value for a related-samples t test (or for any t test,for that matter)?

Accepted Answer

As the degrees of freedom increase, the t-distribution approaches the normal distribution, leading to a decrease in the critical value. This is because the tails of the t-distribution become less heavy, making extreme values less likely.

Question 8

To increase the value of estimated Cohen's d,a researcher increases the sample size.Will this change the value of d?

Accepted Answer

Cohen's d is a measure of effect size that is calculated based on the mean difference between two groups divided by the standard deviation. The formula for Cohen's d does not include sample size, meaning changes in sample size do not directly affect the value of Cohen's d.

Question 9

A researcher selected a sample of 24 participants and observed their behavior at two times.The result of a related-samples t test at a .05 level of significance was t = 2.68.Which of the following correctly describes the result of this test?

Accepted Answer

A related-samples t test is the correct test for this study because the researcher observed the same participants at two different times. The result of the test is significant at a .05 level of significance, with t = 2.68, indicating that there is a significant difference between the participants' behavior at the two times.

Question 10

To compute a related-samples t test,a researcher has to know many values.Which of the following is NOT a value that the researcher must know to compute this test?

Accepted Answer

The population variance of difference scores is not necessary for computing a related-samples t test as it is typically not known. Instead, the researcher estimates the variance using the sample variance of difference scores. The other values listed (estimated standard error for difference scores, sample size or number of pairs of scores, and sample variance of difference scores) are all necessary for the computation of the related-samples t test.

Question 11

A researcher conducts a study in which the population variance of difference scores between two groups is unknown.What type of t test is most appropriate for this study?

Accepted Answer

A related-samples t test, also known as a paired-sample t test, is appropriate when the difference scores between two groups are obtained from the same individuals (i.e., related-samples). This type of t test does not require knowledge of the population variance and is used to compare means between the two related groups.

Question 12

A professor computes the mean difference in exam scores before and after a lecture as 9.0 ± 14.5 (M_D± S_D),and this difference was significant.What is the effect size for this result using estimated Cohen's d?

Accepted Answer

Cohen's d is calculated as the mean difference divided by the standard deviation. Here, d = 9.0 / 14.5 = 0.62. According to Cohen's conventions, 0.2 to 0.5 is a small effect, around 0.5 is a medium effect, and 0.8 and above is a large effect. Therefore, 0.62 is considered a medium effect.

Question 13

A researcher placed male rodents in the presence and absence of a conspecific male.Cortisol (a stress hormone)levels were compared at both times.What type of t test is most appropriate for this study?

Accepted Answer

A related-samples t test would be appropriate for this study because the researcher is comparing cortisol levels before and after exposure to the conspecific male in the same group of rodents.

Question 14

A researcher sampled 25 participants and measured their alcohol consumption (in ounces)in both a home and a bar setting.If the mean difference in satisfaction ratings for this sample was 11.4 ± 2.5 (M_D ± S_MD),then what is the decision at a .05 level of significance?

Accepted Answer

To determine the correct answer, we need to calculate the t-statistic using the given formula:
t = (mean difference - hypothesized difference) / (standard error of the difference)

The hypothesized difference is 0 (no difference between alcohol consumption at home and in a bar setting).

The standard error of the difference is calculated as:

SE = sqrt[ (s1^2/n1) + (s2^2/n2) ]

Where s1 is the standard deviation of the home consumption data, n1 is the sample size for home consumption, s2 is the standard deviation of the bar consumption data, and n2 is the sample size for bar consumption.

We don't have the actual data for calculating these values, but we are given that the mean difference is 11.4 ounces with a standard deviation of 2.5 ounces, and the sample size is 25. Therefore,

SE = sqrt[ (2.5^2/25) + (2.5^2/25) ] = 1.58

Plugging this and the other values into the t formula, we get:

t = (11.4 - 0) / 1.58 = 7.22

This t-value has degrees of freedom (df) equal to n - 1, or 24 in this case. We can look up the critical t-value at a 0.05 level of significance and 24 df in a t-table or calculator, which is approximately 2.064.

Since our calculated t-value (7.22) is greater than the critical t-value (2.064), we can reject the null hypothesis and conclude that there is a significant difference between alcohol consumption at home and in a bar setting. Therefore, the correct answer is B.

Question 15

A researcher sampled 16 couples and measured the mean difference in their marital satisfaction.Each couple was paired and the differences in their ratings (on a 7-point scale)were taken.If the mean difference in satisfaction ratings for this sample was 1.8 ± 2.0 (M_D ± S_D),then what is the decision at a .05 level of significance?

Accepted Answer

The t-value is calculated as (1.8 - 0) / (2.0 / sqrt(16)) = 3.60. With 15 degrees of freedom (n-1 for paired samples), this t-value is significant at the .05 level, indicating a significant difference in satisfaction ratings.

Question 16

All other things being equal,reducing the level of significance from .05 to .01 will ______ the value of the test statistic for a related-samples t test.

Accepted Answer

Reducing the level of significance from .05 to .01 does not affect the value of the test statistic for a related-samples t test. The test statistic is calculated based on the sample data and is independent of the chosen level of significance.

Question 17

A researcher computes the mean difference in locomotion in a sample of 12 rats before and 30 min after an injection of amphetamine.Rats were placed in a box with infrared beams.The number of times rats crossed the beams was used as a measure of locomotion.The mean difference in locomotion was 6.2 ± 8.4 (M_D± S_D)and this difference was significant.What is the effect size for this result using estimated Cohen's d?

Accepted Answer

Cohen's d is calculated as the mean difference divided by the standard deviation. Given a mean difference of 6.2 and a standard deviation of 8.4, Cohen's d = 6.2 / 8.4 = 0.738, which is approximately 0.74. This is considered a medium effect size according to Cohen's conventions.

Question 18

A researcher conditions rats to fear a tone that was sounded just prior to a brief shock.To measure fear following this conditioning,she records the number of lever presses by each rat in the presence and in the absence of the tone.It was hypothesized that reduced lever pressing in the presence of the tone was evidence for a conditioned fear response in rats.If the researcher tested this hypothesis at a .05 level of significance (two-tailed test),then what is her decision if she computes t = -2.842 in a sample of eight rats.

Accepted Answer

The researcher conducted a two-tailed test at a significance level of .05, which means that the critical t-value is +/-2.306 (with df = 7). Since the computed t-value (-2.842) is more extreme (farther from zero) than the critical value (-2.306), we can reject the null hypothesis and conclude that there is evidence for a significant difference in lever pressing between the presence and absence of the tone. Therefore, the conditioned fear response hypothesis is supported.

Question 19

All other things being equal,increasing the sample size will ______ the value of the test statistic for a related-samples t test.

Accepted Answer

Increasing the sample size will generally reduce the standard error of the mean in a related-samples t test, which leads to increased precision in the estimate of the population mean difference. As a result, this increases the value of the test statistic, making it more likely to reject the null hypothesis.

Question 20

Which of the following is an assumption for computing the related-samples t test?

Accepted Answer

All of the options listed are assumptions for computing the related-samples t test. Choice A: The assumption of normal distribution is required for computing the t-test. Choice B: The computation of the t-test involves calculating the variance of difference scores, which is unknown. Choice C: Samples are related or matched within groups, but not between groups. Therefore, all of these assumptions are required for computing the related-samples t test.

Quiz 10: Testing Means: Truehe Related-Samples T Test

A researcher conducts a study in which the same participants are observed across each level of the independent variable.If there are only two levels of the independent variable,then what type of t test is appropriate for this study?

A researcher selects a sample of 36 dog owners and measures their responsiveness to pictures depicting the humane and inhumane treatment of dogs.The researcher finds that responsiveness significantly differed,t = 3.243.Use $\eta$ ² to compute the proportion of variance for this result.

A researcher conducts a study in which different participants are independently observed within groups,and the same participants are observed between groups.If there are only two groups,then what type of t test is appropriate for this study?

Each of the following is needed to compute the estimated Cohen's d,except

A professor compares scores on a competency exam among students at two times during a single semester.What type of t test is most appropriate for this study?

All other things being equal,as the degrees of freedom increase,what happens to the critical value for a related-samples t test (or for any t test,for that matter) ?

To increase the value of estimated Cohen's d,a researcher increases the sample size.Will this change the value of d?

A researcher selected a sample of 24 participants and observed their behavior at two times.The result of a related-samples t test at a .05 level of significance was t = 2.68.Which of the following correctly describes the result of this test?

To compute a related-samples t test,a researcher has to know many values.Which of the following is NOT a value that the researcher must know to compute this test?

A researcher conducts a study in which the population variance of difference scores between two groups is unknown.What type of t test is most appropriate for this study?

A professor computes the mean difference in exam scores before and after a lecture as 9.0 ± 14.5 (M_D± S_D) ,and this difference was significant.What is the effect size for this result using estimated Cohen's d?

A researcher placed male rodents in the presence and absence of a conspecific male.Cortisol (a stress hormone) levels were compared at both times.What type of t test is most appropriate for this study?

A researcher sampled 25 participants and measured their alcohol consumption (in ounces) in both a home and a bar setting.If the mean difference in satisfaction ratings for this sample was 11.4 ± 2.5 (M_D ± S_MD) ,then what is the decision at a .05 level of significance?

All other things being equal,reducing the level of significance from .05 to .01 will ______ the value of the test statistic for a related-samples t test.

All other things being equal,increasing the sample size will ______ the value of the test statistic for a related-samples t test.

Which of the following is an assumption for computing the related-samples t test?

Quiz 10: Testing Means: Truehe Related-Samples T Test

A researcher conducts a study in which the same participants are observed across each level of the independent variable.If there are only two levels of the independent variable,then what type of t test is appropriate for this study?

A researcher selects a sample of 36 dog owners and measures their responsiveness to pictures depicting the humane and inhumane treatment of dogs.The researcher finds that responsiveness significantly differed,t = 3.243.Use η\etaη 2 to compute the proportion of variance for this result.

A researcher conducts a study in which different participants are independently observed within groups,and the same participants are observed between groups.If there are only two groups,then what type of t test is appropriate for this study?

Each of the following is needed to compute the estimated Cohen's d,except

A professor compares scores on a competency exam among students at two times during a single semester.What type of t test is most appropriate for this study?

All other things being equal,as the degrees of freedom increase,what happens to the critical value for a related-samples t test (or for any t test,for that matter) ?

To increase the value of estimated Cohen's d,a researcher increases the sample size.Will this change the value of d?

A researcher selected a sample of 24 participants and observed their behavior at two times.The result of a related-samples t test at a .05 level of significance was t = 2.68.Which of the following correctly describes the result of this test?

To compute a related-samples t test,a researcher has to know many values.Which of the following is NOT a value that the researcher must know to compute this test?

A researcher conducts a study in which the population variance of difference scores between two groups is unknown.What type of t test is most appropriate for this study?

A professor computes the mean difference in exam scores before and after a lecture as 9.0 ± 14.5 (MD ± SD) ,and this difference was significant.What is the effect size for this result using estimated Cohen's d?

A researcher placed male rodents in the presence and absence of a conspecific male.Cortisol (a stress hormone) levels were compared at both times.What type of t test is most appropriate for this study?

A researcher sampled 25 participants and measured their alcohol consumption (in ounces) in both a home and a bar setting.If the mean difference in satisfaction ratings for this sample was 11.4 ± 2.5 (MD ± SMD) ,then what is the decision at a .05 level of significance?

All other things being equal,reducing the level of significance from .05 to .01 will ______ the value of the test statistic for a related-samples t test.

All other things being equal,increasing the sample size will ______ the value of the test statistic for a related-samples t test.

Which of the following is an assumption for computing the related-samples t test?

A researcher selects a sample of 36 dog owners and measures their responsiveness to pictures depicting the humane and inhumane treatment of dogs.The researcher finds that responsiveness significantly differed,t = 3.243.Use $\eta$ ² to compute the proportion of variance for this result.

A professor computes the mean difference in exam scores before and after a lecture as 9.0 ± 14.5 (M_D± S_D) ,and this difference was significant.What is the effect size for this result using estimated Cohen's d?

A researcher sampled 25 participants and measured their alcohol consumption (in ounces) in both a home and a bar setting.If the mean difference in satisfaction ratings for this sample was 11.4 ± 2.5 (M_D ± S_MD) ,then what is the decision at a .05 level of significance?