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PSY 230 Midterm #3 Questions
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A sample of n = 4 scores has SS = 60. What is the variance for this sample?
a) 16
b) 20
c) 30
d) 15
b) 20
On average, what value is expected for the t statistic when the null hypothesis is true?
a) t > 1.96
b) 1
c) 0
d) 1.96
c) 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 in this study?
a) 15
b) 28
c) 29
d) 14
b) 28
What is the average value expected for the independent-measures t statistic if the null hypothesis is true?
a) M1 − M2
b) 0
c) +1 or -1
d) 1
b) 0
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?
a) 14
b) 15
c) 16
d) Cannot be determined from the information given
c) 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?
a) n = 29
b) n = 30
c) n = 31
d) Cannot be determined from the information given
c) n = 31
A research report describing the results of a repeated-measures t test states that "t(22) = 1.71, p > .05." From this report, what was the outcome of the hypothesis test?
a) reject the null hypothesis with a sample of n = 23 participants
b) fail to reject the null hypothesis with a sample of n = 23 participants
c) fail to reject the null hypothesis with a sample of n = 22 participants
d) reject the null hypothesis with a sample of n = 22 participants
b) fail to reject the null hypothesis with a sample of n = 23 participants
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?
a) n = 15 and MD = 2
b) n = 30 and MD = 4
c) n = 30 and MD = 2
d) n = 30 and MD = 2
b) n = 30 and MD = 4
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?
a) The researcher can reject the null hypothesis with α = .05 but not with α = .01
b) The researcher can reject the null hypothesis with either α = .05 or α = .01
c) The researcher must fail to reject the null hypothesis with either α = .05 or α = .01
d) It is impossible to make a decision about the null hypothesis without more information.
c) The researcher must fail to reject the null hypothesis with either α = .05 or α = .01
A repeated-measures study and an independent-measures study both produced a t statistic with df = 10. How many individuals participated in each study?
a) 12 for repeated-measures and 11 for independent-measures
b) 12 for repeated-measures and 12 for independent-measures
c) 11 for repeated-measures and 12 for independent-measures
d) 11 for repeated-measures and 11 for independent-measures
c) 11 for repeated-measures and 12 for independent-measures
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?
a) 4/24
b) 4/13
c) 9/20
d) 9/29
a) 4/24
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?
a) 5
b) 6.25
c) 2.5
d) 25
c) 2.5
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?
a) You must know the population mean.
b) You must know the population variance/standard deviation.
c) You must know the population mean and the variance/standard deviation.
d) The t statistic does not require any information about the population.
d) The t statistic does not require any information about the population.
Which of the following is the correct null hypothesis for a repeated-measures t test?
a) μ1 =μ2
b) MD = 0
c) M1 =M2
d) μD = 0
d) μD = 0
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?
a) 1.73
b) 1.50
c) 0.75
d) 0.19
b) 1.50
What is the pooled variance for the following two samples?
Sample 1: n = 8 and SS = 168
Sample 2: n = 6 and SS = 120
a) 20.57
b) 49
c) 24
d) 7
c) 24
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?
a) 1
b) 3
c) 4
d) 2
d) 2
With α = .01, the two-tailed critical region for a t test using a sample of n = 16 participants would have boundaries of __________.
a) t = ±2.583
b) t = ±2.602
c) t = ±2.947
d) t = ±2.921
c) t = ±2.947
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?
a) 1
b) 2
c) 4
d) Cannot determine without more information
b) 2
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?
a) ±2.080
b) ±2.069
c) ±2.074
d) ±2.064
...
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?
a) 6/2
b) 6/0.50
c) 6/0.25
d) 6/4
a) 6/2
An independent-measures research study uses two samples, each with n = 15 participants. If the data produce a t statistic of t = +2.76, which of the following is the correct decision for a two-tailed hypothesis test?
a) reject the null hypothesis with either α = .05 or α = .01
b) reject the null hypothesis with α = .05 but fail to reject with α = .01
c) Cannot answer without additional information
d) fail to reject the null hypothesis with either α = .05 or α = .01
b) reject the null hypothesis with α = .05 but fail to reject with α = .01
A sample of n = 16 scores produces a t statistic of t = +2.00. If the sample is used to measure effect size with r^2, what value will be obtained for r
^2?
a) 4/19
b) 4/20
c) 2/19
d) 2/2
a) 4/19
For which of the following situations would a repeated-measures research design be appropriate?
a) comparing pain tolerance with and without acupuncture needles
b) comparing self-esteem for students who participate in school athletics versus those who do not
c) comparing verbal problem solving skills for science majors versus art majors
d) comparing mathematical skills for girls versus boys at age 10
a) comparing pain tolerance with and without acupuncture needles
Which of the following research situations would be most likely to use an independent-measures design?
a) compare the blood-pressure readings before medication and after medication for a group of patients
b) examine the development of vocabulary as a group of children mature from age 2 to 3
c) examine the long-term effectiveness of a stop-smoking treatment by interviewing participants 2 and 6 months after the treatment ends
d) compare the mathematics skills for 9th grade boys versus 9th grade girls
d) compare the mathematics skills for 9th grade boys versus 9th grade girls
Compared to an independent-measures design, a repeated-measures study is more likely to find a significant effect because it reduces the contribution of variance due to __________.
a) individual differences
b) time-related factors
c) the effect of the treatment
d) order effects
a) individual differences
In general, what is the effect of an increase in the variance of difference scores for the sample?
a) an increase in the standard error and a decrease in the value of t
b) an increase in the standard error and an increase in the value of t
c) a decrease in the standard error and an increase in the value of t
d) a decrease in the standard error and a decrease in the value of t
a) an increase in the standard error and a decrease in the value of t
Under what circumstances can a very small treatment effect be statistically significant?
a) if the sample size is small and the sample variance is big
b) if the sample size and the sample variance are both small
c) if the sample size is big and the sample variance is small
d) if the sample size and the sample variance are both big
c) if the sample size is big and the sample variance is small
One sample has n = 10 scores and a variance of s^2 = 20, and a second sample has n = 15 scores and a variance of s^2 = 30.
What can you conclude about the pooled variance for these two samples?
a) It will be closer to 20 than to 30.
b) It will be closer to 30 than to 20.
c) It will be exactly halfway between 20 and 30.
d) Cannot be determined without more information
b) It will be closer to 30 than to 20.
What is assumed by the homogeneity of variance assumption?
a) The two samples have equal variances.
b) The two populations have equal variances.
c) The two sample variances are not equal.
d) The two population variances are not equal.
...
For a repeated-measures study, as the sample mean difference increases, the likelihood of rejecting the null hypothesis also increases.
True
False
True
Repeated-measures designs are particularly well-suited to research studies examining learning or other changes that occur over time.
True
False
True
If the two samples are the same size, then the pooled variance will equal the average of the two sample variances.
True
False
True
When the population variance or standard deviation is not known, you must use a t statistic instead of a z-score for a hypothesis test.
True
False
True
For an independent-measures t statistic, the estimated standard error measures how much difference is reasonable to expect between the sample means for two samples selected from the same population.
True
False
True
In the repeated-measures t statistic, the value for the estimated standard error in the denominator is computed entirely from the sample data.
True
False
True
As the sample size is increased, the t distribution becomes flatter and more spread out.
True
False
False
A research study compares the mean weight for a sample of n = 36 participants before they begin a 6-week diet and their mean weight at the end of the diet. This is an example of an independent-measures design.
True
False
False
The homogeneity of variance assumption states that the two population variances are equal.
True
False
True
If the 90% confidence interval for μ is from 40 to 50, then the sample mean is M = 45.
True
False
True
Briefly explain the advantages and disadvantages of using a repeated-measures design as opposed to an independent-measures design.
Advantages of repeated-measures test:
Requires fewer participants (each participant is in both sets of scores) (especially helpful with rare populations)
Indicates changes over time
Eliminates problems due to individual differences (e.g. age, IQ, personality, etc.)
Disadvantages of repeated-measures test: would include the individuals of population or group having shaped or influenced ideas and could be untruthful of there changes throughout the data period
A researcher conducts an independent-measures study examining the effectiveness of a group exercise program at an assisted living facility for elderly adults. One group of residents is selected to participate in the program, and a second group serves as a control. After 6 weeks, the researcher records a combined score measuring balance and strength for each individual (higher scores = better balance and strength). The data are as follows:
Control group: n = 10, M = 12, SS = 120.5
Exercise group: n = 15, M = 15.5, SS = 190.0
a. What is the pooled variance?
b. What is the estimated standard error?
c. What is the t score for this study?
d. Compute Cohen's d to measure the size of the treatment effect.
A. Pooled Variance:
(120.5) + (190.0) / (9) + (14) = 13.5
B. Estimated Standard Error:
square root of (120.5 / 10-1) / (10) + (190.0 / 15-1) / (15) = 1.62
C. t-score
D. Cohen's D
;