Statistics - Exam 3
In a sample of 17 participants, a researcher estimates the 90% CI for a sample with a mean of = 7 and an estimated standard error for the difference scores of 2.2. What is the confidence interval at this level of confidence?
90% CI 3.2, 10.8
In a sample of 14 participants, a researcher estimates the 90% CI for a sample with a mean of M1 - M2 = 10.7 and an estimated standard error for the difference () of 2.9. What is the confidence interval at this level of confidence?
90% CI 5.5, 15.9
In a sample of 30 participants, a researcher estimates the 95% CI for a sample with a mean of M1 - M2 = 0.7 and an estimated standard error for the difference () of 0.2. What is the confidence interval at this level of confidence?
95% CI 0.3, 1.1
In a sample of 28 participants, a researcher estimates the 95% CI for a sample with a mean of M = 1.5 and an estimated standard error () of 0.3. What is the confidence interval at this level of confidence?
95% CI 0.9, 2.1
In a sample of 20 participants, a researcher estimates the 99% CI for a sample with a mean of = 3.7 and an estimated standard error for the difference scores of 0.2. What is the confidence interval at this level of confidence?
99% CI 3.1, 4.3
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?
A related-samples t test is the correct test for this study; the result of the test is significant.
What are the degrees of freedom for the related-samples t test?
(nD-1)
State the critical value(s) for a t test using a .05 level of significance in the lower tail only: t(24).
+- 1.711
A researcher matched 30 participants on intelligence (hence 15 pairs of participants), and then compared differences in emotional responsiveness to two experimental stimuli between each pair. For this test, what are the critical values, assuming a two-tailed test at a .05 level of significance?
+- 2.145
State the critical value(s) for a t test using a two-tailed test at a .05 level of significance: t(20).
+-2.086
A researcher records the level of attention among 18 students during an interactive and lecture portion of a single class. If she computes a related-samples t test at a .05 level of significance (two-tailed test), then what are the critical values for this test?
+-2.110
A researcher records the strength of a conditioned response among 12 rats in the presence and absence of conditioned cues. If he computes a related-samples t test at a .05 level of significance (two-tailed test), then what are the critical values for this test?
+-2.201
In a sample of 26 participants, a researcher estimates the 90% CI for a sample with a mean of = 0.6 and an estimated standard error for the difference scores of 0.1. What is the upper confidence limit for this interval?
0.77
In a sample of 18 participants, a researcher estimates the 80% CI for a sample with a mean of M1 - M2 = 8.8 and an estimated standard error for the difference () of 1.8. What is the upper confidence limit for this interval?
11.2
A researcher reports that the effectiveness of a new marketing campaign significantly increased sales compared with the previous campaign strategy, t(49) = 2.562, p < .05. Use eta-squared to interpret the effect size for this result.
12% of the variability in marketing effectiveness can be accounted for by the new marketing strategy.
In a sample of 20 participants, a researcher estimates the 95% CI for a sample with a mean of M = 5.4 and an estimated standard error () of 1.6. What is the lower confidence limit for this interval?
2.1
In a sample of 26 participants, a researcher estimates the 90% CI for a sample with a mean of = 0.6 and an estimated standard error for the difference scores of 1.1. What is the upper confidence limit for this interval?
2.5
A researcher selects a sample of 32 participants who are assigned to participate in a study with one group. What are the degrees of freedom for this test?
31
A researcher reports with 90% confidence that 31-37% of Americans believe in ghosts. What is the point estimate for this interval?
34%
In a sample of 18 participants, a researcher estimates the 80% CI for a sample with a mean of M1 - M2 = 8.8 and an estimated standard error for the difference () of 1.8. What is the lower confidence limit for this interval?
6.4
"Elementary school children spent significantly more time reading the presence of a teacher than when the teacher was absent, t(7) = 2.804, p < .05 ( =?4 0.46)." In this related-samples t test, how many participants were observed?
8
In a sample of 20 participants, a researcher estimates the 95% CI for a sample with a mean of M = 5.4 and an estimated standard error () of 1.6. What is the upper confidence limit for this interval?
8.8
In a sample of 12 participants, a researcher estimates the 80% CI for a sample with a mean of M = 22.3 and an estimated standard error () of 4.7. What is the confidence interval at this level of confidence?
80% CI 15.9, 28.7
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 , then what is the decision at a .05 level of significance?
Alcohol consumption significantly differed, t(24) = 4.56.
A researcher records the crying time (in minutes) of infants given oral administration of sucrose (n = 12) or tap water (n = 16) prior to a heel prick. The mean crying time in the sucrose group was 3.3 ± 2.4 (M ± SD) min; in the tap water group, it was 7.3 ± 1.6 (M ± SD) min. If the null hypothesis is that there is no difference in crying time, then what is the decision for this test?
Crying time was significantly reduced among infants given the sucrose solution prior to a heel prick.
A professor teaches a certain section of material using a lot of examples with sports and cars to illustrate. He is concerned that this may have biased his instruction to favor male students. To test this, he measures exam grades from this section of material among women (n = 10) and men (n = 10). The mean score in the male group was 84 ± 4.0 (M ± SD); in the female group, it was 78 ± 8.0 (M ± SD) points. If the null hypothesis is that there is no difference in exam scores, then test the null hypothesis at a .05 level of significance for a two-tailed test.
Exam scores were significantly higher in the male group, t(18) = 2.12, p < .05.
Which figure below depicts data from a study on child play behavior with a smaller value for error variance?
Figure A
Is a one-sample t test reported differently for one-tailed and two-tailed tests?
No, the same values are reported
A researcher finds that the mean difference in productivity between employees working the morning shift (n = 16) and the night shift (n = 10) is 5.0 units, and the estimated standard error for the difference is 2.7 units. If the null hypothesis states that there is no difference in productivity, then is this result significant at a .05 level of significance for a two-tailed test?
No, this result is not significant
A researcher has participants rate the likability of a sexually promiscuous person described in a vignette as being male (n = 20) or female (n = 12). The mean likability ratings in each group were 4.0. If the null hypothesis is that there is no difference in likability ratings, then do likability ratings differ at a .05 level of significance?
No, this result is not significant, t(30) = 0
To increase the value of estimated Cohen's d, a researcher increases the sample size. Will this change the value of d?
No; the sample size is not used to compute effect size.
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= ñ2.842 in a sample of 8 rats?
Reject the null hypothesis; there is evidence for a conditioned fear response.
Two researchers (A and B) compute a one-sample t test. For both tests, the mean difference between the sample and value stated in the null hypothesis is 5, but the standard error is smaller for Researcher A. Which test is more likely to result in a decision to reject the null hypothesis?
Researcher A
Two researchers (A and B) compute a two-independent-sample t test. For both tests, the mean difference between the two groups is 10, but the standard error is smaller for Researcher A. Which test is more likely to result in a decision to reject the null hypothesis?
Researcher A
Two researchers (A and B) compute a two-independent-sample t test. For both tests, the standard error is the same, but the mean difference between the groups is larger for Researcher A. Which test is more likely to result in a decision to reject the null hypothesis?
Researcher A
Two researchers (A and B) compute a one-sample t test. For both tests, the standard error is the same, but the mean difference between the sample and value stated in the null hypothesis is smaller for Researcher A. Which test is more likely to result in a decision to reject the null hypothesis?
Researcher B
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)?
Retain the null hypothesis; responses were not more accurate under hypnosis.
A researcher conducts a study and concludes that a new behavioral health treatment program significantly reduces one's risk for disease compared with risk levels in the general population (d = -0.64). Interpret the size of this effect.
Risk levels in the population shifted 0.64 standard deviations below the mean.
A researcher measures deviant behavior in a sample of 12 children from abusive homes (Sample A). Another researcher measures the same behavior in a sample of 18 children from abusive homes (Sample B). Which sample is associated with larger degrees of freedom?
Sample B
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 , then what is the decision at a .05 level of significance?
Satisfaction ratings significantly differ, t(15) = 3.60.
A researcher conducts two t tests. Test 1 is a two-tailed test with a smaller sample size at a .05 level of significance. Test 2 is a two-tailed test with a larger sample size at a .05 level of significance. What do you know about the degrees of freedom for each test?
Test 2 is associated with larger degrees of freedom
A researcher conducts two t tests. Test 1 is a two-tailed test with a smaller sample size at a .05 level of significance. Test 2 is a two-tailed test with a larger sample size at a .05 level of significance. What do you know about the degrees of freedom for each test?
Test 2 is associated with larger degrees of freedom.
A researcher conducts two t tests. Test 1 is a one-tailed test with a smaller sample size at a .05 level of significance. Test 2 is a one-tailed test with a larger sample size at a .05 level of significance. What do you know about the critical values for each test?
Test 2 is associated with smaller critical values
The mean crying time of infants during naptime at a local preschool is 12 min. The school implements a new naptime routine in a sample of 25 infants and records an average crying time of 8 ± 4.6 (M±SD) min. Test whether this new naptime routine reduced crying time at a .05 level of significance.
The new naptime routine significantly reduced crying time, t(24) = -4.35, p < .05.
Two researchers analyze the same data set. Researcher A uses a two-independent-sample t test and decides to retain the null hypothesis. Researcher B uses a related-samples t test and decides to reject the null hypothesis. Which of the following is a likely explanation for the disparity in the decisions made?
The related-samples t test had greater power to detect the effect.
How does the test statistic differ for a t test using the repeated-measures versus the matched-samples design?
The test statistic for the repeated-measures and the matched-samples designs do not differ; the test statistic is computed the same.
A local elementary school determined that the average number of volunteers for their "Step into Spring" annual fundraiser has been 14 persons on average (per event). After taking additional measures to recruit volunteers this year, they got 28 people to volunteer. Test whether these additional measures increased the number of volunteers at a .05 level of significance.
There is not enough information to answer this question
The average response time to a bank robbery is about 9 min. A local community wants to improve on this time, so they implement advanced training seminars. They find that the new response time for a sample of 36 police officers is 8 ± 4.2 (M±SD) min. Test whether this advanced training seminar reduced response time at a .05 level of significance.
This advanced training seminar did not reduce response time, t(35) = -1.43, p > .05.
A researcher reports that stress levels among nurses are higher compared to stress levels in the general population, t (20) = 2.086, p = .05 (d = .12). Was this a one-tailed or a two-tailed test?
Two-tailed test because the p value is equal to .05.
A researcher selects a sample of 16 women and asks them to rate how important a sense of humor is in someone they want a long-term relationship with. She records scores averaging 1.6 ± 0.8 (M ± SD) on a rating scale from -3 (not important at all) to +3 (very important). Assuming that an average score of 0 is the null hypothesis, test whether or not women find this trait important at a .05 level of significance.
Women found this trait to be important, and this result was significant, t(15) = 8.00, p < .05.
A point estimate is typically reported with an interval estimate. Why?
all of these
Computing a one-sample t test is appropriate when ______.
all of these
Computing a two-independent-sample t test is appropriate when ______.
all of these
For the related-samples t test, assuming that all other values remain constant, then as samples size increases, ______.
all of these
The t distribution is similar to the z distribution except ______.
all of these
Which of the following is an advantage for selecting related samples compared to selecting independent samples in behavioral research?
all of these
Which of the following is an assumption for computing any type of independent sample t test?
all of these
Which of the following is an assumption for computing the related-samples t test?
all of these
State the critical value(s) for a t test using a .05 level of significance in the lower tail only: t(24).
approximately 1.711
The related-samples design can ______.
be more practical
It is most appropriate to report effect size with a significant result. Why is it generally inappropriate to report effect size with nonsignificant results?
because it makes little sense to report the size of an effect that you just concluded does not exist
A research design in which different participants are observed one time in each group of a research study is called ______.
between-subjects design
State the critical value(s) for the following two-tailed t test at a .05 level of significance: t(infinity).
both B and C
Which of the following explains why point estimation can be a useful procedure to estimate a population mean?
both B and C
A researcher reports that the mean time it takes to complete an experimental task is 1.4 ± 8.0 (M ± SD) s. If the null hypothesis was that the mean equals 1.0, then what is the effect size for this test using estimated Cohen's d?
d = 0.05; small effect size
A researcher reports that mean ratings of liking for some food are 0.8 ± 2.4 (M ± SD). If the null hypothesis was that the mean equals 0, then what is the effect size for this test using estimated Cohen's d?
d = 0.33; medium effect size
A researcher reports that the mean difference in response time to an auditory versus a visual cue is 0.83 s, with a pooled sample variance equal to 2.45. What is the effect size for this test using estimated Cohen's d?
d = 0.53; medium effect size
A professor computes the mean difference in exam scores before and after a lecture as 9.0 ± 14.5 , and this difference was significant. What is the effect size for this result using estimated Cohen's d?
d = 0.62 (medium effect)
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 , and this difference was significant. What is the effect size for this result using estimated Cohen's d?
d = 0.74 (medium effect)
A researcher reports that the mean difference in the body weight of rats following a pharmacological versus control treatment is 14 g, with a pooled sample variance equal to 256. What is the effect size for this test using estimated Cohen's d?
d = 0.88; large effect size
The test statistic for a related-samples t test makes tests concerning a single sample of ______.
difference scores
Which of the following is an assumption for the two-independent sample t test, but not the one-sample t test?
equal variances
Which type of error is used to compute the confidence interval for one sample selected from a population with an unknown variance?
estimated standard error
Which of the following is the denominator of the test statistic for the related-samples t test?
estimated standard error for difference scores
Which type of error is used to compute the confidence interval for two independent samples selected from at least one population with an unknown variance?
estimated standard error for the difference
Which type of error is used to compute the confidence interval for two related samples selected from at least one population with an unknown variance?
estimated standard error for the difference scores
A statistical procedure in which a sample statistic is used to estimate the value of an unknown population parameter is called ______.
estimation
A researcher reports a significant effect in some population. If he computes both an eta-squared and an omega-squared effect size estimate, then which estimate will be the largest?
eta-squared
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.
have no effect on
All other things being equal, increasing the sample size will ______ the value of the test statistic for a related-samples t test.
increase
Each of the following is an advantage for using the related-samples design, except ______.
it increases the variability measured in a study
A researcher asks a sample of brothers and sisters to rate how positive their family environment was during childhood. In this study, the differences in ratings between each brother and sister pair were compared. The type of design described here is called a ______.
matched-samples design
Which of the following is a type of related-samples design in which different participants are observed in each group, but treated statistically as if they are the same persons in each group?
matched-samples design
Which of the following identifies a large effect size for a t test?
n^2 = .25
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-squared to compute the proportion of variance for this result.
n^2 = 0.23
A researcher reports a significant effect with t(14) = 3.24. Compute eta-squared for this result.
n^2 = 0.43 (large effect size)
When reporting data in a results section, it is ______ necessary to identify the type of t test computed.
not
A researcher reports a significant mean difference in a given population. If she computes both eta-squared and omega-squared to measure the effect size, then which estimate will be the most conservative?
omega-squared
A researcher conducts a study comparing the obesity rate in a small community to the known obesity rate in the United States. Assuming that the population variance in unknown, what type of t test is appropriate for this study?
one-sample t test
A researcher records the number of distracters (such as noises) that preschool-aged children ignore while watching a popular Sunday morning cartoon show. Assuming that the population variance is unknown, what type of t test is appropriate for this study?
one-sample t test
You read about a study testing whether night shift workers sleep the recommended 8 hr per day. Assuming that the population variance of sleep (per day) is unknown, what type of t test is appropriate for this study?
one-sample t test
One difference between a repeated-measures design and a matched-samples design is that ______.
only one design involves observing the same participants in each group
The more that scores in each group ______, the larger the error variance.
overlap
The denominator of the test statistic for a related-samples t test ______.
provides an estimate of the error associated with the difference scores
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?
related-samples t test
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?
related-samples t 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?
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?
related-samples t test
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?
related-samples t test
A type of factor in which different participants are observed in each group, or at each level of the factor, is called ______.
repeated measures factor
A researcher compares the difference in the amount of texting by students in class during the first week and last week of classes. The type of design described here is called a ______.
repeated-measures design
A researcher records the time it takes (in seconds) for participants to respond (by pressing a key) to a familiar and an unfamiliar word flashed onto a computer screen. In this study, the difference in response time for each participant is compared. The type of design described here is called a ______.
repeated-measures design
A type of related-samples design in which participants are observed more than one time is called a ______.
repeated-measures design
The estimated standard error in the t statistic uses the ______ to estimate the ______ when the population variance is unknown.
sample variance; population variance
Eta-squared is computed ______ for the one-sample, and the two-independent-sample t tests.
similarly
The less that scores overlap between groups, the ______ the error variance.
smaller
The ______ is an inferential statistic used to determine the number of standard deviations in a t distribution that a sample mean deviates from the mean value or mean difference stated in the null hypothesis.
t statistic
Which of the following summarizes a t test that was significant and associated with a large effect size?
t(12) = 2.95, p < .05, d = .82
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)?
the critical value decreases
All other things being equal, as the sample size increases, what happens to the critical value for a related-samples t test (or for any t test, for that matter)?
the critical value decreases
Using APA format, which value is typically given in parentheses when reporting the results for a t test?
the degrees of freedom
A researcher reports that college students consume an average of 3.6 alcoholic drinks per week. What is the interval estimate in this example?
the interval estimate is not given
Which of the following is the numerator of the test statistic for the related-samples t test?
the mean difference observed minus the mean difference stated in a null hypothesis
To compute a two-independent-sample 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?
the pooled population variance
As a requirement for the t test, researchers compute any type of t test with samples selected from populations in which ______.
the population variance is unknown
To compute a one-sample 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?
the population variance must be known
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?
the population variance of difference scores
Each of the following is needed to compute the estimated Cohen's d, except ______.
the standard error
Which of the following best describes the goal of estimation?
to narrow in on the true population mean by defining limits within which it is likely to be contained
A professor compares final exam scores in his psychology class to final exam grades in another comparable professor's class. Assuming that the population variance of exam scores is unknown, what type of t test is appropriate for analyzing differences between these classes?
two-independent sample t test (two-independent sample t test is not discussed in this chapter.)
A researcher compares differences in mean health scores between students at two local high schools. Assuming that the population variance is unknown, what type of t test is appropriate for this study?
two-independent-sample t test
A researcher conducts a study measuring differences in brain activity among rats placed on either a continuous or intermittent reward schedule. Assuming that the population variance in unknown, what t test is appropriate for this study?
two-independent-sample t test
A researcher records differences in ratings of emotion among participants watching either a drama or a romance film. Assuming that the population variance is unknown, what type of t test is appropriate for this study?
two-independent-sample t test
A researcher reports that stress levels among nurses are higher compared to stress levels in the general population, t(20) = 2.086, p = .05 (d = .12). Was this a one-tailed or a two-tailed test?
two-tailed test because the p value is equal to .05
A researcher selects a sample of 24 college students and has them rate their liking for two advertisements aimed at improving the image of the college. The researcher finds that liking ratings significantly differed, t = 2.900. Use omega-squared to compute the proportion of variance for this result.
w^2 = .24
Compared to the two-independent-sample t test, the related-samples design decreases ______.
standard error
Each of the following is an estimate of error for a t test, except ______.
standard error
Which measure of effect size is most commonly reported with a t test?
Cohen's d
Is a one-sample t test reported differently for one-tailed and two-tailed tests?
No, the same values are reported.
A key difference between a t statistic and a z statistic is that the standard error is ______ to compute a t statistic.
estimated
The related-samples design can ______ the power to detect an effect by making the standard error ______.
increase; smaller
