Statistics: Exam 3
State the critical value(s) for a t test using a .05 level of significance in the lower tail only: t(24)
-1.711
Which measure of effect size is most commonly reported with a t test?
Cohen's d
What are the degrees of freedom for the related samples t test?
(nD-1)
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 (SM) of 1.6. What is the lower confidence limit for this interval?
2.1
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 (SM1-M2) of -.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 (SM) of 0.3. What is the confidence interval at this level of confidence?
95% CI 0.9, 2.1
The test statistic for a related samples t test makes 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
A key difference between a t statistic and a z statistic is that the standard error is _______ to compute a t statistic
Estimated
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
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 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 test or a two-tailed test?
Two tailed test because the p value is equal to .05.
State the critical value(s) for a t test using a two-tailed test at a .05 level of significance: t(20)
±2.086
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 reports with 90% confidence that 31% to 37% of Americans believe in ghosts. What is the point estimate for this interval?
34%
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 (SM) 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 (SM) of 4.7. What is the confidence interval at this level of confidence?
80% CI 15.9, 28.7
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 actually observed in each group, but treated statistically as if they are the same persons in each group?
Matched samples design
Computing a two-independent sample t test is appropriate when -Different participants are assigned to each group -The population variance is unknown -Participants are observed one time -All of the above
All of the above
The related samples design can _______________
Be more practical
State the critical value(s) for the following two-tailed t test at a .05 level of significance: t(∞). ±1.645 ±1.96 -The same as for a two-tailed z test at a .05 level of significance -Both B and C
Both B and C
Which of the following explains why point estimation can be a useful procedure to estimate a population mean? -It defines the range of scores within which the population mean is likely to be contained -The sample mean is equal to the population mean on average -The sample mean is an unbiased estimator of the population mean -Both B and C
Both B and C
All other things being equal, increasing the sample size will _______________ the value of the test statistic for a related samples t test.
Increase
Is a one-sample t test reported differently for one-tailed and two-tailed tests?
No, the same values are reported
A researcher records the time it takes (in seconds) for participants to respond (by pressing a key) to a familiar versus 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 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
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
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 the null hypothesis
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 additional measures increased the number of volunteers at a .05 level of significance.
There is not enough information to answer this question.
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 two-tailed test?
Two-tailed test because the p value is equal to .05
A researcher computes the mean difference in locomotion in a sample of 12 rats before and 30 minutes 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 (MD±SD), 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 pharmacological versus control treatments is 14 grams, 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
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
A researcher selects a sample of 32 participants who are assigned to participate in a study with two groups. What are the degrees of freedom for this test?
30
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
Which of the following is an assumption for computing the related samples t test? -The population being sampled from is normally distributed -The population variance of difference scores is unknown -Samples are related or matched between groups, but not within groups -All of the above
All of the above
It is most appropriate to report effect size with a significant result. Why is it generally inappropriate to report effect size with insignificant results?
Because it makes little sense to report the size of an effect that you just concluded doesn't exist
A research design in which different participants are observed at one time in each group of a research study is called
Between-subjects design
A type of factor in which different participants are observed in each group, or at each level of the factor, is called
Between-subjects factor
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
The related samples design can __________ the power to detect an effect by making the standard error ___________
Increase; smaller
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
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
You read about a study testing whether night shift workers sleep the recommended 8 hours 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 type of related samples design in which participants are observed more than once is called a
Repeated measures design
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
The average response time to a bank robbery is about 9 minutes. A local community wants to improve on this time, so they implement advanced training seminars. They find that they new response time for a sample of 36 police officers is 8±4.2 (M±SD) minutes. 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
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 each exam scores is unknown, what type of t test is appropriate for analyzing differences between these classes?
Two-independent sample t test
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
Which of the following identifies a large effect size for a t test?
n²=.25
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
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 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
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
Each of the following is an estimate of error for a t test, except
Standard error
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
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
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
A point estimate is typically reported with an interval estimate. Why? -Using only a point estimate is associated with low certainty -The interval estimate gives researchers a higher level of confidence -The interval estimate adds certainty to the estimate of the population mean -All of the above
All of the above
Which of the following is an assumption for computing any type of independent sample t test? -Data in the population being sampled are normally distributed -Data were obtained from a sample that was selected using a random sampling procedure -The probabilities of each measured outcome in a study are independent -All of the above
All of the above
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
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
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
The estimated standard error in the t statistic uses the ________ to estimate the ________ when the population variance is unknown.
Sample variance; population variance
The mean crying time of infants during naptime at a local preschool is 12 minutes. The school implements a new naptime in a sample of 25 infants and records an average crying time of 8±4.6 (M±SD) minutes. 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
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 t test
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
Computing a one-sample t test is appropriate when -Participants are assigned to only one group -The population variance is unknown -Participants are observed one time -All of the above
All of the above
For the related samples t test, assuming that all other values remain constant, then as samples size increases -The value of the test statistic increases -The power to detect an effect increases -The estimate for standard error decreases -All of the above
All of the above
The t distribution is similar to the z distribution except -It is associated with greater variability -It is characterized by "thicker" tails compared with the z distribution -It is associated with scores being more likely in the tails of the distribution -All of the above
All of the above
Which of the following is an advantage for selecting related samples compared to selecting independent samples in behavioral research? -Selecting related samples can be more practical -Selecting related samples minimizes standard error -Selecting related samples increases power -All of the above
All of the above
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
Each of the following is an advantage for using the related samples design, except
It increases the variability measured in a study
Compared to the two-independent sample t test, the related samples design decreases
Standard error
Using APA format, which value is typically given in parentheses when reporting the results for a t test?
The degrees of freedom
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
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
Each of the following is needed to compute the estimated Cohen's d, except
The standard error
A researcher reports that mean ratings of linking 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 selects a sample of 36 dog owners and measures their responsiveness to pictures depicting the human 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
n²=0.23
A researcher matched 30 participants on intelligence (hence 15 pairs of patients), 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
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±D) 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 researcher reports that the mean time it takes to complete an experimental task is 1.4±8.0 (M±SD) seconds. 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 the mean difference in response time to an auditory versus a visual cue is 0.83 seconds, 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 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.
w²=0.24
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 is the critical value for this test?
±2.110
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 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
"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 (w²=0.46)." In this related samples t test, how many participants were observed?
8
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
To compute a related samples t test, a researcher has to know many values. Which of the following is NOT a value the researcher must know to compute this test?
The population variance of difference scores
A researcher conducts a study measuring comparing the obesity rate in a small community to the known obesity rate in the United States. Assuming that the population variance is unknown, what type of t test is appropriate for this study?
One-sample t test
A researcher reports a significant effect with t(14)=3.24. Compute eta-squared for this result
n²=0.43 (large effect size)
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
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
A professor computes the mean difference in exam scores before and after a lecture a 9.0±14.5 (MD±SD), and this difference was significant. What is the effect size for this result suing estimated Cohen's d?
d=0.62 (medium effect)
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 is unknown, what t test is appropriate for this study?
Two-independent sample t test
