Deck 9: Testing Means: One-Sample and Two-Independent-Sample T Tests

Question 1

You read about a study testing whether night shift workers sleep the recommended 8 hr/day.Assuming that the population variance of sleep (per day)is unknown,what type of t test is appropriate for this study?

A) one-sample t test
B) two-independent-sample t test
C) There is not enough information to answer this question.

Answer 1

one-sample t test

Question 2

As a requirement for the t test,researchers compute any type of t test with samples selected from populations in which

A) the population variance is known.
B) the population size is very large.
C) the population variance is unknown.
D) the population is the same size as the sample.

Answer 2

the population variance is unknown.

Question 3

State the critical value(s)for the following two-tailed t test at a .05 level of significance: t( $\infty$ ).

A) ±1.645
B) ±1.96
C) the same as for a two-tailed z test at a .05 level of significance
D) ±1.96 and the same as for a two-tailed z test at a .05 level of significance

Answer 3

±1.96 and the same as for a two-tailed z test at a .05 level of significance

Question 4

The estimated standard error in the t statistic uses the ______ to estimate the ______ when the population variance is unknown.

A) sample variance; population variance
B) population variance; sample variance
C) standard error; sample variance
D) degrees of freedom; sample size

Question 5

A key difference between a t statistic and a z statistic is that the standard error is ______ to compute a t statistic.

A) removed
B) replaced
C) estimated
D) placed in the numerator

Question 6

The t distribution is similar to the z distribution,except

A) it is associated with greater variability.
B) it is characterized by "thicker" tails compared with the z distribution.
C) it is associated with scores being more likely in the tails of the distribution.
D) all of these.

Question 7

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?

A) one-sample t test
B) two-independent-sample t test
C) There is not enough information to answer this question.

Question 8

Which of the following is an assumption for computing any type of independent-sample t test?

A) Data in the population being sampled are normally distributed.
B) Data were obtained from a sample that was selected using a random sampling procedure.
C) The probabilities of each measured outcome in a study are independent.
D) All of these.

Question 9

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.

A) t distribution
B) t statistic
C) standard error
D) degrees of freedom

Question 10

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?

A) Test 1 is associated with smaller critical values.
B) Test 2 is associated with smaller critical values.
C) Each test is associated with the same critical values.
D) It depends; there is not enough information to answer this question.

Question 11

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?

A) 32
B) 30
C) 31
D) There is not enough information to answer this question.

Question 12

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?

A) one-sample t test
B) two-independent-sample t test
C) There is not enough information to answer this question.

Question 13

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.

A) Women found this trait to be important, and this result was significant, t(16) = 8.00, p < .05.
B) Women found this trait to be important, and this result was significant, t(15) = 8.00, p < .05.
C) Women did not find this trait to be important, p > .05.
D) There is not enough information to answer this question.

Question 14

State the critical value(s)for a t test using a .05 level of significance in the lower tail only: t(24).

A) ±1.711
B) -1.711
C) ±2.064
D) -2.064

Question 15

State the critical value(s)for a t test using a two-tailed test at a .05 level of significance: t(20).

A) ±1.725
B) ±2.093
C) ±2.086
D) ±0.687

Question 16

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?

A) Test 1 is associated with larger degrees of freedom.
B) Test 2 is associated with larger degrees of freedom.
C) Each test is associated with the same degrees of freedom.
D) It depends; there is not enough information to answer this question.

Question 17

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.

A) This advanced training seminar significantly reduced response time, t(35) = 11.43, p < .05.
B) This advanced training seminar significantly reduced response time, t(35) = -1.43, p < .05.
C) This advanced training seminar did not reduce response time, t(35) = -1.43, p > .05.
D) There is not enough information to answer this question.

Question 18

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 type of t test is appropriate for this study?

A) one-sample t test
B) two-independent-sample t test
C) There is not enough information to answer this question.

Question 19

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.

A) The new naptime routine significantly reduced crying time, t(24) = -4.35, p < .05.
B) The new naptime routine did not reduce crying time, t(24) = -4.35, p < .05.
C) The new naptime routine did not reduce crying time, t(24) = 8.67, p > .05.
D) The new naptime routine significantly reduced crying time, t(24) = 8.67, p < .05.

Question 20

Computing a one-sample t test is appropriate when

A) participants are assigned to only one group.
B) the population variance is unknown.
C) participants are observed one time.
D) all of these.

Question 21

A researcher measures mean health scores of children at a local school and compares these scores to the mean health score known in the general population.Assuming that the population variance is unknown,what type of t test is appropriate for this study?

A) one-sample t test
B) two-independent-sample t test
C) There is not enough information to answer this question.

Question 22

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?

A) d = 0.05; small effect size
B) d = 0.50; medium effect size
C) d = 1.05; large effect size
D) there is not enough information to answer this question

Question 23

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?

A) Crying time was significantly reduced among infants given the water solution prior to a heel prick.
B) Crying time was not reduced among infants given the sucrose solution prior to a heel prick.
C) Crying time was significantly reduced among infants given the sucrose solution prior to a heel prick.
D) Crying time was the same in both groups.

Question 24

A researcher reports a significant effect in some population.If she computes both an $\eta$ ² and an $\omega$ ² effect size estimate,then which estimate will be the largest?

A) $\eta$ ²
B) $\omega$ ²
C) It depends on the sample size.
D) It depends on the value of the t statistic.

Question 25

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?

A) The estimated standard error must be known.
B) The population variance must be known.
C) The sample size must be known.
D) The sample mean and sample variance must be known.

Question 26

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.

A) Yes, because the number of volunteers doubled; this is a significant increase.
B) No, this is not a significant increase because the error term is too large.
C) This would have been significant if it were a two-tailed test.
D) There is not enough information to answer this question.

Question 27

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?

A) d = 0.33; small effect size
B) d = 0.33; medium effect size
C) d = 3.00; large effect size
D) There is not enough information to answer this question.

Question 28

Computing a two-independent-sample t test is appropriate when

A) different participants are assigned to each of two groups.
B) the population variance is unknown.
C) participants are observed one time in a given group.
D) all of these.

Question 29

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?

A) Researcher A.
B) Researcher B.
C) The likelihood is the same for both researchers.
D) There is not enough information to answer this question.

Question 30

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?

A) the pooled sample variance
B) the pooled population variance
C) the sample size for both samples
D) the sample mean for both samples

Question 31

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 estimates 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?

A) Yes, this result is significant.
B) No, this result is not significant.
C) There is not enough information to answer this question.

Question 32

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.

A) Exam scores were significantly higher in the male group, t(18) = 2.83, p < .05.
B) Exam scores were the same between groups, t(18) = 2.12, p > .05.
C) Exam scores were significantly higher in the male group, t(18) = 2.12, p < .05.
D) Exam scores were the same between groups, t(18) = 1.00, p > .05.

Question 33

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?

A) Researcher A.
B) Researcher B.
C) The likelihood is the same for both researchers.
D) There is not enough information to answer this question.

Question 34

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?

A) Yes, this result is significant, p < .05.
B) No, this result is not significant, t(30) = 0.
C) No, this result is not significant, t(30) = 1.00.
D) There is not enough information to answer this question because the variance in each sample is not given.

Question 35

A researcher reports a significant effect with t(14)= 3.24.Compute $\eta$ ² for this result.

A) $\eta$ ² = 0.43 (large effect size)
B) $\eta$ ² = 0.43 (medium effect size)
C) $\omega$ ² = 0.37 (large effect size)
D) $\omega$ ² = 0.37 (medium effect size)

Question 36

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.

A) 64% of the variability in risk level can be accounted for by the new treatment.
B) 64% of the new treatment can be accounted for by the risk levels.
C) Risk levels in the population shifted 0.64 standard deviations below the mean.
D) Risk levels in the population shifted 0.64 standard deviations above the mean.

Question 37

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?

A) Researcher A.
B) Researcher B.
C) The likelihood is the same for both researchers.
D) There is not enough information to answer this question.

Question 38

It is most appropriate to report effect size with a significant result.Why is it generally inappropriate to report effect size with nonsignificant results?

A) Because insignificant results will always have an effect size equal to 0.
B) Because insignificant results indicate that an effect size is also not significant.
C) Because it makes little sense to report the size of an effect that you just concluded doesn't exist.
D) Because the probability of the size of an effect varies depending on the significance of the effect size measure.

Question 39

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?

A) one-sample t test
B) two-independent-sample t test
C) There is not enough information to answer this question.

Question 40

Which of the following is an assumption for the two-independent-sample t test,but not the one-sample t test?

A) normality
B) random sampling
C) independence
D) equal variances

Question 41

When testing a hypothesis with one or two groups selected from a population with an unknown variance,a t test is appropriate.

Question 42

$\eta$ ² is computed ______ for the one-sample and the two-independent-sample t tests.

A) differently
B) infinitely
C) similarly
D) semantically

Question 43

As the degrees of freedom for a t test increase,the critical values for that test also increase.

Question 44

A researcher reports a significant mean difference in a given population.If she computes both $\eta$ ² and $\omega$ ² to measure the effect size,then which estimate will be most conservative?

A) $\eta$ ²
B) $\omega$ ²
C) It depends on the sample size.
D) It depends on the value of the t statistic.

Question 45

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?

A) d = 0.53; medium effect size
B) d = 0.53; large effect size
C) d = 0.34; small effect size
D) d = 0.34; medium effect size

Question 46

Which measure of effect size is most commonly reported with a t test?

A) $\eta$ ²
B) $\omega$ ²
C) t statistic
D) Cohen's d

Question 47

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 $\eta$ ² to interpret the effect size for this result.

A) 12% of the variability in marketing effectiveness can be accounted for by the new marketing strategy.
B) 12% of the standard error can be accounted for by the effectiveness of the marketing strategy.
C) Marketing effectiveness shifted 0.12 standard deviations above the mean in the population.
D) 12% of the variability in marketing effectiveness can be accounted for by the new marketing strategy and 12% of the standard error can be accounted for by the effectiveness of the marketing strategy.

Question 48

Is a one-sample t test reported differently for one-tailed and two-tailed tests?

A) No, the same values are reported.
B) It depends on whether the results were significant.
C) Yes, only significant results for a two-tailed test are reported.
D) It can be reported differently when the effect size is large.

Question 49

Normality is the assumption that data in the population are normally distributed.

Question 50

Normality,random sampling,and independence are all assumptions for the one-sample t test.

Question 51

A t statistic estimates the standard error by using the sample variance to approximate the population variance.

Question 52

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?

A) d = 0.06; small effect size
B) d = 0.08; small effect size
C) d = 0.88; large effect size
D) There is not enough information to answer this question.

Question 53

A t distribution with infinite degrees of freedom is a z distribution.

Question 54

A t test is associated with N degrees of freedom.

Question 55

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?

A) Researcher A.
B) Researcher B.
C) The likelihood is the same for both researchers.
D) There is not enough information to answer this question.

Question 56

A t test is associated with n - 1 degrees of freedom.

Question 57

A researcher reports the following result for a two-tailed test at a .05 level of significance,t(20)= 2.010,and correctly decides to reject the null hypothesis.

Question 58

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?

A) One-tailed test because the p value is equal to .05.
B) Two-tailed test because the p value is equal to .05.
C) It could be a one- or a two-tailed test.

Question 59

Which of the following summarizes a t test that was significant and associated with a large effect size?

A) t(22) = 3.02, p < .05, d = .36
B) t(30) = 1.03, p > .05, d = .20
C) t(60) = 1.76, p > .05, d = .45
D) t(12) = 2.95, p < .05, d = .82

Question 60

A researcher must know the population variance in order to compute a t test.

Question 61

If d = 0.28,then we conclude that mean scores in some population have shifted 0.28 standard deviations below the mean.

Question 62

A one-sample t test will be undefined (denominator = 0)when the same score is recorded for all participants in a study.

Question 63

The p value is reported with the test statistic of a one-sample and a two-independent-sample t test using APA format.

Question 64

A two-independent-sample t test is used when the same participants are observed two times.

Question 65

Effect size measures are an estimate of the size of an effect in a population.

Question 66

When the difference between two groups is compared,the pooled standard deviation is used as an estimate for the population standard deviation in the effect size formula for estimated Cohen's d.

Question 67

$\eta$ ² is a more conservative estimate than $\omega$ ².

Question 68

An estimated Cohen's d is interpreted in terms of the number of standard deviations that an effect shifted in some population.

Question 69

A one-sample t test will be t = 0 when the mean difference is equal to 0.

Question 70

When scores are measured in a single group,the sample standard deviation is used as an estimate of the population standard deviation in the effect size formula for estimated Cohen's d.

Question 71

A researcher reports that the mean difference between two groups is 20.12 and the estimated standard error for the difference is 2.83.Hence,the conclusion must be to reject the null hypothesis for a two-tailed test at a .05 level of significance.

Question 72

A researcher computes a two-independent-sample t test and finds that the result is undefined (the denominator is equal to 0).This always happens when two groups do not differ (i.e.,the mean difference is equal to 0).

Question 73

A two-independent-sample t test is computed when mean differences are compared between two or more groups sampled from a population with an unknown variance.

Question 74

A researcher reports the following result for a lower-tail critical test at a .05 level of significance,t(40)= 1.512,and accurately concludes to reject the null hypothesis.

Question 75

Measures of proportion of variance are computed the same for all t tests.

Question 76

When the proportion of variance explained by some treatment is larger than 0.25,we conclude that there is a large effect in the population.

Question 77

A one-sample t test will be t = 0 when the standard error is equal to 0.

Question 78

Cohen's d is a measure of proportion of variance.

Question 79

The critical values are reported with the test statistic of a one-sample and a two-independent-sample t test using APA format.

Question 80

A researcher reports the following result for a two-tailed test at a .05 level of significance,t(30)= 2.020,and correctly decides to retain the null hypothesis.