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Which of the following is a fundamental difference between the t statistic and a z-score?
The t statistic uses the sample variance in place of the population variance.
Which of the following is not needed to compute a t statistic?
The value of the population variance or standard deviation
Why are t statistics more variable than z-scores?
The extra variability is caused by variations in the sample variance
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?
The t statistic does not require any information about the population.
If two samples are selected from the same population, under what circumstances will the two samples have exactly the same t statistic?
If the samples are the same size and have the same mean and the same variance
A sample of n = 4 scores has SS = 60. What is the variance for this sample?
20
On average, what value is expected for the t statistic when the null hypothesis is true?
0
What is the sample variance and the estimated standard error for a sample of n = 9 scores with SS = 72?
s2 = 9 and sM = 1
A sample of n = 9 scores has a variance of s2 = 36. What is the estimated standard error for the sample mean?
2
A sample of n = 25 scores has a mean of M = 40 and a standard deviation of s = 10. What is the estimated standard error for the sample mean?
2
A sample with a mean of M = 40 and a variance of s2 = 20 has an estimated standard error of 1 point. How many scores are in the sample?
20
A sample of n = 16 scores has a mean of M = 65 and an estimated standard error of 2 points. What is the sample variance?
s2 = 64
Which set of characteristics will produce the smallest value for the estimated standard error?
A large sample size and a small sample variance
Which of the following samples will have the smallest value for the estimated standard error?
n = 16 with s2 = 16
A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 30, how many individuals were in the sample?
n = 31
A researcher conducts a hypothesis test using a sample of n = 20 from an unknown population. What is the df value for the t statistic?
19
When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?
It is flatter and more spread out than the normal distribution.
With α = .01, the two-tailed critical region for a t test using a sample of n = 16 subjects would have boundaries of ______.
t = ±2.947
With α = .05 and df = 8, the critical values for a two-tailed t test are t = ±2.306. Assuming all other factors are held constant, if the df value were increased to df = 20, what would happen to the critical values for t?
They would decrease (move closer to zero).
A researcher is using a two-tailed hypothesis test with α = .05 to evaluate the effect of a treatment. If the boundaries for the critical region are t = ± 2.080, then how many individuals are in the sample?
n = 22
A sample has a mean of M = 39.5 and a standard deviation of s = 4.3, and produces a t statistic of t = 2.14. For a two-tailed hypothesis test with α = .05, what is the correct statistical decision for this sample?
It is impossible to make a decision about H0 without more information.
A sample of n = 25 scores produces a t statistic of t = 2.062. If the researcher is using a two-tailed test, which of the following is the correct statistical decision?
The researcher must fail to reject the null hypothesis with either α = .05 or α = .01.
A hypothesis test produces a t statistic of t = 2.20. If the researcher is using a two-tailed test with α = .05, how large does the sample have to be in order to reject the null hypothesis?
At least n = 13
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?
The sample with the smaller variance will produce the larger t statistic.
If other factors are held constant, which set of sample characteristics is most likely to produce a significant t statistic?
n = 100 with s2 = 100
If other factors are held constant, what is the effect of increasing the sample size?
It will decrease the estimated standard error and increase the likelihood of rejecting H0.
If other factors are held constant, what is the effect of increasing the sample variance?
It will increase the estimated standard error and decrease the likelihood of rejecting H0.
If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that = 80?
M = 90 and small sample variance
A researcher selects a sample from a population with = 30 and uses the sample to evaluate the effect of a treatment. After treatment, the sample has a mean of M = 32 and a variance of s2 = 6. Which of the following would definitely increase the likelihood of rejecting the null hypothesis?
a.
Increase the number of individuals in the sample
b.
Increase the sample mean
c.
Decrease the sample variance
d.
All of the other options will increase the likelihood of rejecting the null hypothesis.
If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that = 80?
M = 90 for a sample of n = 100
Under what circumstances can a very small treatment effect be statistically significant?
If the sample size big and the sample variance is small
How does sample variance influence the estimated standard error and measures of effect size such as r2 and Cohen's d?
Larger variance increases the standard error but decreases measures of effect size.
A researcher selects a sample from a population with = 30 and uses the sample to evaluate the effect of a treatment. After treatment, the sample has a mean of M = 32 and a variance of s2 = 6. If Cohen's d is used to measure the size of the treatment effect, which of the following would have no effect on the value of Cohen's d?
Increase the number of individuals in the sample
Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen's d. How will the outcomes for the two samples compare?
The larger sample is more likely to reject the hypothesis, but the two samples will have the same value for Cohen's d.
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?
r2 = 4/19
If other factors are held constant, how does sample size influence the likelihood of rejecting the null hypothesis and measures of effect size such as r2 and Cohen's d?
A larger sample increases the likelihood but has little influence on measures of effect size
If other factors are held constant, how does sample variance influence the likelihood of rejecting the null hypothesis and measures of effect size such as r2 and Cohen's d?
Larger sample variance increases both the likelihood and measures of effect size.
A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?
d = 0.50
A sample is selected from a population with μ = 70, and a treatment is administered to the sample. After treatment, the sample mean is M = 74, and Cohen's d is d = 1.00. What is the value of the sample variance?
s2 = 16
Which of the following describes what a confidence interval does?
It uses a sample mean to estimate the corresponding population mean.
What value is estimated with a confidence interval using the t statistic?
The value for an unknown population mean
If a sample of n = 16 scores is being used to make an 80% confidence interval estimate of the population mean, μ, what value(s) of t should be used?
t = ±1.341
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 μ?
μ = 40 ± 2.353(2)
Which combination of factors would definitely increase the width of a confidence interval?
Increase the sample mean and increase the percentage of confidence
Which of the following would have no effect on the width of a confidence interval?
Increase the sample mean
The results of a hypothesis test are reported as follows: t(15) = 2.70, p < .05. Based on this report, how many individuals were in the sample?
16
Which of the following is the correct way to report the results of a hypothesis test and a measure of effect size using a t statistic?
t(19) = 2.30, p < .05, r2 = 0.42,
A researcher selects a sample from a population with a mean of = 40 and administers a treatment to the individuals in the sample. If the treatment is expected to decrease scores, which of the following is the correct statement of the null hypothesis for a one-tailed test?
μ= > 40
A hypothesis test with a sample of n = 25 participants produces a t statistic of t = +2.53. Assuming a one-tailed test with the critical region in the right-hand tail, what is the correct decision?
The researcher can reject the null hypothesis with either α = .05 or α = .01.
With α = .05, what is the critical t value for a one-tailed test with n = 15?
t = 1.761
Which of the following research situations would be most likely to use an independent-measures design?
Compare the mathematics skills for 9th-grade boys versus 9th-grade girls
If an independent-measures design is being used to compare two treatment conditions, then how many different groups of participants would be needed and how many scores would there be for each participant?
2 groups, 1 score each
Which of the following is the correct null hypothesis for an independent-measures t test?
μ1 - μ2 = 0
An independent-measures study uses n = 15 participants in each group to compare two treatment conditions. What is the df value for the t statistic for this study?
28
An independent-measures study has one sample with n = 6 and a second sample with n = 8 to compare two experimental treatments. What is the df value for the t statistic for this study?
12
An independent-measures research study uses a total of 40 participants to compare two treatment conditions. What is the df value for the t statistic for this study?
38
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?
10
A researcher reports an independent-measures t statistic with df = 30. If the two samples are the same size (n1 = n2), then how many individuals are in each sample?
n = 16
A researcher reports an independent-measures t statistic with df = 16. How many participants were in the entire study?
18
One sample of n = 8 scores has a variance of s2 = 6 and a second sample of n = 8 scores has s2 = 10. If the pooled variance is computed for these two samples, then the value obtained will be ______.
exactly halfway between 6 and 10
What is the pooled variance for the following two samples?
Sample 1: n = 8 and SS = 168
Sample 2: n = 6 and SS = 120
24
One sample has a variance of s2 = 10 and a second sample has a variance of s2 = 6. Which of the following most accurately describes the pooled variance for the two samples?
Somewhere between 6 and 10
One sample has n = 10 scores and a variance of s2 = 20, and a second sample has n = 15 scores and a variance of s2 = 30. What can you conclude about the pooled variance for these two samples?
It will be closer to 30 than to 20.
Two samples, each with n = 5 scores, have a pooled variance of 40. What is the estimated standard error for the sample mean difference?
4
Two samples each have n = 4 scores. If the first sample has a variance of 10 and the second sample has a variance of 6, what is the estimated standard error for the sample mean difference?
2
One sample has n = 5 scores and the second has n = 10 scores. If the pooled variance for the two samples is 30, what is the value of the estimated standard error for the sample mean difference?
3
The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 18. If there are n = 4 scores in each sample, what is the estimated standard error for the sample mean difference?
3
An independent-measures study with n = 6 in each sample produces a sample mean difference of 4 points and a pooled variance of 12. What is the value for the t statistic?
2
Two samples, each with n = 16 scores, produce an estimated standard error of 4 points and a t statistic of t = 2.00. What is the sample mean difference?
8
The data from an independent-measures research study produce a sample mean difference of 6 points and an estimated standard error of 2 points. If there are n = 8 scores in each sample, what is the value for the t statistic?
6/2
What is the average value expected for the independent-measures t statistic if the null hypothesis is true?
0
An independent-measures research study uses two samples, each with n = 10 participants. If the data produce a t statistic of t = 2.095, which of the following is the correct decision for a two-tailed hypothesis test?
Fail to reject the null hypothesis with either α = .05 or α = .01
An independent-measures research study uses two samples, each with n = 15 participants. If the data produce a t statistic of t = 2.760, which of the following is the correct decision for a two-tailed hypothesis test?
Reject the null hypothesis with α = .05 but fail to reject with α = .01
Two samples, each with n = 8, produce an independent-measures t statistic of t = -2.15. Which of the following decisions is justified for a two-tailed test?
Reject H0 with α = .05 but fail to reject with α = .01
A researcher reports t(22) = 5.30, p < .01 for an independent-measures experiment. How many individuals participated in the entire experiment?
24
The results of an independent-measures research study are reported as "t(22) = 2.12, p < .05, two tails." For this study, what t values formed the boundaries for the critical region?
±2.074
An independent-measures research study with n = 5 participants in each treatment produces sample variances of 8 and 10, and a 2-point difference between the two treatment means. Given this information, what is the value of Cohen's d?
2/3
Two samples, each with n = 9 scores, produce an independent-measures t statistic of t = 2.00. If the effect size is measured using r2, what is the value of r2?
4/20
One sample has M = 18 and a second sample has M = 14. If the pooled variance for the two samples is 16, what is the value of Cohen's d?
1.00
An independent-measures study produces sample means of M1 = 20 and M2 = 17, and a pooled variance of 9. For this study, what is Cohen's d?
d = 3/3
An independent-measures study produces sample means of M1 = 20 and M2 = 17. If both samples have n = 18 scores and Cohen's d = 0.50, what is the value for the pooled variance?
36
An independent-measures study comparing two treatment conditions with n = 6 in each sample produces t = 4.00. What is the value of r2 for this study?
16/26
A researcher predicts that scores in treatment A will be higher than scores in treatment B. If the mean for the 10 participants in treatment A is 4 points higher than the mean for the 10 participants in treatment B and the data produce t = 2.095, what decision should be made?
With = .05, reject H0 for a one-tailed test but fail to reject for a two-tailed test
A researcher predicts that scores in treatment A will be higher than scores in treatment B. Which of the following is the correct null hypothesis for a one-tailed test evaluating this prediction?
μA <= μB
The narrower the confidence interval, the more precise it is. With this in mind, which combination of factors will produce the most precise estimate of the difference between two population means?
Two samples of n = 50 and 80% confidence
Two separate samples are being used to estimate the population mean difference between two treatment conditions. Which of the following would produce the widest confidence interval?
n1 = n2 = 10 with a pooled variance of 100
Using an independent-measures t, the 90% confidence interval for the difference between two population means ranges from 19 to 23. Based on this confidence interval, how big is the difference between the two sample means?
21 points
Which of the following confidence intervals also indicates a significant difference between treatments with α = .05?
Estimate that μ1 - μ2 is in an interval between 2 and 10 with 95% confidence
For the independent-measures t statistic, what is the effect of increasing the sample variances?
Decrease the likelihood of rejecting H0 and decrease measures of effect size
For the independent-measures t statistic, what is the effect of increasing the difference between sample means?
Increase the likelihood of rejecting H0 and increase measures of effect size
For an independent-measures t statistic, what is the effect of increasing the number of scores in the samples?
Increase the likelihood of rejecting H0 and have little or no effect on measures of effect size
Which of the following sets of data would produce the largest value for Cohen's d?
n = 20 for both samples, a pooled variance of 15, and a mean difference of 5 points
Which of the following sets of data would produce the largest value for an independent-measures t statistic?
The two sample means are 10 and 20, with variances of 20 and 25
If other factors are held constant, which of the following sets of data would produce the largest value for an independent-measures t statistic?
The two samples both have n = 30, with sample variances of 20 and 25
Which combination of factors is most likely to produce a significant value for an independent-measures t statistic?
Large samples and small variance
If other factors are held constant, which of the following sets of data is most likely to produce a significant mean difference?
A sample mean difference of 10 points with n = 10 for both samples
Which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic and a large measure of effect size?
A large mean difference and small sample variances
Assuming that there is a 5-point difference between the two sample means, which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic?
Large sample sizes and small sample variances
What is assumed by the homogeneity of variance assumption?
The two populations have equal variances.
If other factors are held constant, which of the following sets of data is most likely to satisfy the homogeneity of variance assumption?
A sample mean difference of 6 points and sample variances of 15 and 10
A sample mean difference of 4 points and sample variances of 9 and 6
A sample mean difference of 2 points and sample variances of 6 and 4
The other 3 options are equally likely to satisfy the assumption.
For which of the following situations would a repeated-measures research design be appropriate?
Comparing pain tolerance with and without acupuncture needles
A researcher plans to conduct a research study comparing two treatment conditions with a total of 20 participants. Which of the following designs would produce 20 scores in each treatment?
A repeated-measures design
A repeated-measures study uses a total of n = 10 participants to compare two treatment conditions. How many scores are measured in this study, and how many scores are actually used to compute the sample mean and the sample variance?
20 measured and 10 used
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
3
The following data were obtained from a repeated-measures research study. What is the value of SS for the difference scores?
Subject 1st 2nd
#1 10 11
#2 4 6
#3 7 9
#4 6 5
6
A repeated-measures study using a sample of n = 20 participants would produce a t statistic with df = ____.
19
A research study produces a t statistic with df = 14. For this study, which of the following designs would require a total of 30 participants?
A matched-subjects design
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?
df = 19
A repeated-measures study and an independent-measures study both produced a t statistic with df = 10. How many individuals participated in each study?
11 for repeated-measures and 12 for independent-measures
A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10. How many individuals participated in each study?
11 for repeated and 22 for matched
A matched-subjects study and an independent-measures study both produced a t statistic with df = 10. How many individuals participated in each study?
22 for matched-subjects and 12 for independent-measures
For the repeated-measures t statistic, df = _____.
n - 1
Which of the following is the correct null hypothesis for a repeated-measures t test?
µD = 0
If the null hypothesis is true, what value is expected on average for the repeated-measures t statistic?
0
For a repeated-measures study, if the null hypothesis is true, then what value should be obtained for the sample mean.
MD near 0
The null hypothesis for a repeated-measures test states,
the entire population will have a mean difference of μD = 0.
A repeated-measures study comparing two treatments with n = 4 participants produces MD = 2 and SS = 75 for the difference scores. What is the estimated standard error for the sample mean difference?
2.5
What is the value of the estimated standard error for the following set of D-scores?
Scores: 2, 2, 10, 2
2
For a repeated-measures study comparing two treatments with a sample of n = 9 participants, the difference scores have a mean of MD = 4.90 with SS = 72. What is the estimated standard error for the sample mean difference?
1
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 MD = 4 with SS = 12 for the difference scores. What is the estimated standard error for the sample mean difference?
1
For a repeated-measures study comparing two treatment conditions, a researcher obtains a sample of n = 9 difference scores with a mean of MD = 4 and a variance of s2 = 36. What is the value for the repeated-measures t statistic for these data?
4/2
A repeated-measures study comparing two treatments with a sample of n = 4 participants produces MD = 3 with SS = 48 for the set of difference scores. What is the repeated-measures t statistic for these data?
3/2 = 1.50
If a repeated-measures study shows a significant difference between two treatments with
α = .01, then what can you conclude about measures of effect size?
A significant effect does not necessarily mean that the effect size will be large.
A sample of difference scores has a mean of MD = 5 with a variance of s2 = 100. If effect size is measured using Cohen's d, what is the value of d?
d = 5/10
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?
MD = 2
A researcher obtains t(20) = 2.00 and MD = 9 for a repeated-measures study. If the researcher measures effect size using the percentage of variance accounted for, what value will be obtained for r2?
4/24
A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 16 participants and obtains a t statistic of t = 1.94. The treatment is expected to increase scores and the sample mean shows an increase. Which of the following is the correct decision for a hypothesis test using α = .05.
Reject the null hypothesis with a one-tailed test but fail to reject with two tails
A researcher obtains t = 2.25 for a repeated-measures study using a sample of
n = 10 participants. Based on this t value, what is the correct decision for a two-tailed test?
Fail to reject the null hypothesis with either α = .05 or α = .01
A research report describing the results from a repeated-measures study states that the data show no significant difference between the two treatments, t(10) = 1.65, p > .05. Based on this report, how many individuals participated in the research study?
11
A research report describing the results from a repeated-measures t test states that "t(22) = 1.71, p > .05." From this report, what was the outcome of the hypothesis test?
Fail to reject the null hypothesis with a sample of n = 23 participants
A researcher reports t(12) = 2.86, p < .05 for a repeated-measures research study. How many individuals participated in the study?
n = 13
In general, if the variance of the difference scores increases, what will happen to the value of the t statistic?
It will decrease (move toward 0 at the center of the distribution).
A researcher uses a repeated-measures design to compare individuals' performance before treatment with their performance after treatment. If all of the participants show improved performance of 8 or 9 points after treatment, what should the researcher find?
The variance of the difference scores is near zero.
In general, what is the effect of an increase in the variance for the sample of difference scores?
An increase in the standard error and a decrease in the value of t
In general, what characteristics of the difference scores are most likely to produce a significant t statistic for the repeated-measures hypothesis test?
A large number of scores and a small variance
What is indicated by a large variance for a sample of difference scores?
An inconsistent treatment effect and a low likelihood of a significant difference
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 ______.
a small variance for the difference scores and a small standard error
If other factors are held constant, which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?
n = 30 and SS = 10 for the difference scores
Assuming that other factors are held constant, which of the following would tend to increase the likelihood of rejecting the null hypothesis?
Increase the sample mean difference
If other factors are held constant, which of the following sets of data is most likely to produce a significant value for the repeated-measures t statistic?
n = 30 and MD = 4
Which of the following describes the effect of increasing sample size?
There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis increases.
Which of the following describes the effect of an increase in the variance of the difference scores?
Measures of effect size and the likelihood of rejecting the null hypothesis both decrease.
What value is estimated with a confidence interval using the repeated-measures t statistic?
The mean for a population of difference scores
A sample of n = 9 college students is used to evaluate the effectiveness of a new Study Skills Workshop. Each student's grade point average (GPA) is recorded for the semester before the workshop and for the semester after the workshop. The average GPA improved by MD = 0.60 points with s2 = 0.09. The researcher would like to use the sample to estimate how much effect the workshop would have for the entire college population. Which of the following is the 80% confidence interval for these data?
µD = 0.60 + 0.10(1.397)
Which of the following will not increase the width of a confidence interval?
Increase the sample mean from MD = 2 to MD = 4
If the sample size is held constant, which of the following will produce the widest 90% confidence interval for the population mean difference for a repeated-measures study?
MD = 3 with s2 = 20 for the difference scores
Which of the following possibilities is a serious concern with a repeated-measures study?
The results will be influenced by order effects.
Compared to an independent-measures design, a repeated-measured study is more likely to find a significant effect because it reduces the contribution of variance due to ______.
individual differences
For which of the following situations would a repeated-measures design have the maximum advantage over an independent-measures design?
When very few subjects are available and individual differences are large
In a repeated-measures experiment, each individual participates in one treatment condition and then moves on to a second treatment condition. One of the major concerns in this type of study is that participation in the first treatment may influence the participant's score in the second treatment. What is this problem is called?
Order effects
;