Psychology statistics exam 3

A teacher gives a reading skills test to a third-grade class of n = 41 children at the beginning of the school year. To evaluate the changes that occur during the year, students are tested again at the end of the year. Their test scores showed an average improvement of MD =4.9 points with s 2 = 82. A. Are the results sufficient to conclude that there is significant improvement in children's reading skills? Use a one-tailed test with α = .01. B. If there is a significant effect, compute Cohen's d to measure the size of the effect. C. Write a conclusion demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report in APA style.

A. H0 : There is no significant improvement in children's reading skills. (i.e., MD <= 0) H1 :There is a significant improvement in children's reading skills.(i.e., MD > 0) •The standard error: Sq.Root of 82/41= 1.41 •t = 4.9/1.41 = 3.48 •t critical for df = 40 and p <.01 (1-tail test) is 2.423 Reject H0. B. s = √ s2 = √82= 9.06; Cohen's d = MD /s =4.9/9.06= 0.54; this is a medium size effect. C. There was a significant improvement in children's reading skills at the end of the school year, t(40) = 3.46, p <.01, estimated Cohen's d = 0.54

In a repeated-measures study with a sample of n = 9 participants, the difference scores have a mean of MD = 4.90 and SS = 72. What is the estimated standard error for the study? A. 1.0 B. 3.0 C. 9.0 D. None of the above.

A. 1.0

The following data were obtained from a repeated-measures study of memory performance before and after drinking 2 cups of coffee. What is the value of mean difference MD for these data? Participant Before After #1 10 15 #2 4 8 #3 7 5 #4 6 11 A. 3.0 (or -3.0) B. 3.5 (or -3.5) C. 4.0 (or -4.0) D. None of the above.

A. 3.0 (or -3.0)

Two samples, each with n = 5 scores, have a pooled variance, sp2 = 40. What is the estimated standard error, s(M1-M2) for the sample mean difference? A. 4 B. 8 C. 10 D. 20 E. None of the above.

A. 4

Which of the following research situations would be most likely to use a between subjects research design? A. Examining differences in reading comprehension among middle school children of two ethnic groups. B. Investigating the long-term effectiveness of a stop-smoking treatment by comparing participants craving for cigarettes after 2 months and 6 months of treatment. C. Examining academic performance of the Texas State University students by comparing their mean GPA to the national average GPA of undergraduate population in the U.S. D. All of the above.

A. Examining differences in reading comprehension among middle school children of two ethnic groups.

An independent-measures research study examines gender differences in toddlers' verbal skills. The researchers tested verbal skills of nine 2-years old girls (i.e., n 1 = 9) and nine 2-years old boys (i.e., n 2 = 9). The data produced the t(16) = -1.98. Which of the following is the correct decision for a two-tailed hypothesis test with p <.05? A. Fail to reject the H0 with p < .05; there is no significant gender difference in toddlers' verbal skills. B. Reject the H0 with p < .05; there is no significant gender difference in toddlers' verbal skills. C. Fail to reject the H0 with p < .05; there is a significant gender difference in toddlers' verbal skills. D. Reject the H0 with p < .05; there is a significant gender difference in toddlers' verbal skills.

A. Fail to reject the H0 with p < .05; there is no significant gender difference in toddlers' verbal skills.

Which of the following is an accurate definition of a Type II error? A. Failing to reject a false null hypothesis B. Failing to reject a true null hypothesis C. Rejecting a true null hypothesis. D. Rejecting a false null hypothesis.

A. Failing to reject a false null hypothesis

A researcher conducts an independent samples 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 assessed physical fitness of each participant. The data are as follows: Exercise Group: Control Group: n = 15 n = 15 M = 37 M = 34 SS = 230 SS = 160 A. Does the exercise program have a significant effect on physical fitness? Use p < .05, 2-tails test. B. If there is a significant effect, compute the estimated Cohen's d to measure the size of the treatment effect. C. Write a conclusion demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report in APA style.

A. H0: µ1 = µ2 (The exercise program had no significant effect on physical fitness) H1: µ1 =/ µ2 (The exercise program had a significant effect on physical fitness) The pooled variance: sp2 = (230 + 160/(15-1) + (15-1) = 390/28 = 13.9 The estimated standard error: sM1-M2 = Sq Root of 13.9/15 +13.9/15 = Sq. Root of 1.85 = 1.36 t = (37 - 34)/1.36= 2.21 t critical for df = 28 and p <.05, 2-tails test is 2.048 Reject H0. B. estimated Cohen's d = 3/√13.9 = 3/3.73= 0.80; this is a large effect. C. The group exercise program had a significant positive effect on physical fitness of elderly adults (i.e., physical fitness of elderly adults improved), t(28) = 2.21, p <.05, estimated Cohen's d = 0.80.

A sample is selected from a population with mean of µ = 62. After a treatment is administered to the individuals in the sample, the sample mean is M = 68 and the standard deviation is s = 12. A. Assume that the sample size is n = 9. - Compute a single sample t-test and the estimated Cohen's d effect size. - Based on your computed t test value, can you reject H0 with a two-tailed test α = .05? - Write the value of t critical, your decision about H0 & conclusion (i.e., is the treatment significant or not?) B. Assume the sample size is n = 25. - Compute a single sample t-test and the estimated Cohen's d effect size. - Based on your computed t test value, can you reject H0 with a two-tailed test α = .05? - Write the value of t critical value, your decision about H0 & conclusion (i.e., is the treatment significant or not?) C. Compare your answers to A & B (i.e., the decision about H0 & conclusion and estimated Cohen's d) and describe how increasing the size of the sample affected the likelihood of rejecting the H0 and the size of estimated Cohen's d.

A. If n = 9, the estimated standard error: SM = s/SqRoot of n = 12/SqRoot of 9 = 4.0 t = (M - µ)/ SM = (68-62)/4.0 = 1.5 estimated Cohen's d = (M - µ)/s = (68-62)/12 = 6/12 = 0.5 for df = n - 1 = 8, the critical t value for p <. 05, 2-tailed test is 2.306 Failed to Reject H0. The treatment has no significant effect. B. If n = 25, the estimated standard error,: SM = s/SqRoot of n = 12/SqRoot of 25 = 12/5 = 2.4 t = (M - µ)/ SM = (68-62)/2.4 = 2.5 estimated Cohen's d = (M - µ)/s = (68-62)/12 = 0.5 For df = n - 1 = 24, the critical t value is t = 2.064, p < .05 2-tailed test. Reject H0 . The treatment has a significant effect. C. Increasing the sample size increased the likelihood of rejecting H0 (ie., the treatment was found to be significant with n = 25 but not with n = 9) but it had no effect on the value of estimated Cohen's d effect size. (Note: If the sample was very small, n = 9, even a medium size effect (i.e., estimated Cohen's d = 0.5) was not found to be statistically significant).

The estimated standard error, s(M1-M2) in the t-test for independent samples ________________. A. Is computed based on the variances, s2 of both samples B. Is computed based on the variance, s2 of a larger sample C. Is computed based on the variance, s2 of the smaller sample D. Is computed based on the population variances, σ2

A. Is computed based on the variances, s2 of both samples

Which of the following is the correct null hypothesis for an independent samples t-test (assume 2-tails test)? A. There is no difference between populations represented by two samples (i.e., μ1 - μ2 = 0 or μ1 = μ2). B. There is a difference between populations represented by two samples (i.e., μ1 - μ2 ≠ 0 or μ1 ≠ μ2). C. There is no difference between two samples (i.e., M1 - M2 = 0 or M1 = M2). D. None of the above.

A. There is no difference between populations represented by two samples (i.e., μ1 - μ2 = 0 or μ1 = μ2).

A sample is selected from a population with μ = 87, and a treatment is administered to the sample. After treatment, the sample mean is M = 92 with a sample variance of s2 = 36. Based on this information, what is the effect size evaluated by the estimated Cohen's d? A. d = 0.83 B. d = 0.75 C. d = 0.55 D. d = 0.35 E. None of the above.

A. d = 0.83

What is the average value expected for the independent-measures t statistic ifthe null hypothesis is true (i.e., the two samples represent the same population)? A. t = 0 B. t >1 C. t = 1 D. Can't be determined without moreinformation

A. t = 0

What is indicated by a large variance for a sample of difference scores (i.e., a large variance of D scores)? A. An inconsistent treatment effect and a high likelihood of a significant difference. B. An inconsistent treatment effect and a low likelihood of a significant difference. C. A consistent treatment effect and a low likelihood of a significant difference. D. A consistent treatment effect and a high likelihood of a significant difference.

An inconsistent treatment effect and a low likelihood of a significant difference.

A researcher reports t(14) = 2.86, p <.05 2-tails test for a repeated-measures research study. How many participants are in the study? A. n = 14 B. n = 15 C. n = 16 D. n = 28 E. None of the above.

B. n = 15

An independent-measures study uses two samples of n = 15 participants in each group to compare two treatment conditions. What is the df value for the t statistic for this study? A. 19 B. 20 C. 28 D. 38 E. None of the above.

C. 28

A sample of n = 36 scores has a mean of M = 40 and a standard deviation of s = 24. What is the estimated standard error for a single sample t-test? A. 6 B. 5 C. 4 D. 1 E. None of the above

C. 4

Two samples, each with n = 9 scores, produce an independent samples t statistic of t(16) = 2.00, p <.05 with one-tail test. If the effect size is measured using r2 , what is the value of r2 ? A. 2/16 B. 4/16 C. 4/20 D. 2/18

C. 4/20

The results of a hypothesis test with the t-test for a single sample are reported as follows: t(60) = 3.70, p < 05., 2-tailed test. Based on this report, how many individuals were in the sample? A. 120 B. 60 C. 61 D. 59 E. None of the above

C. 61

If other factors are held constant, what is the effect of decreasing the variability of scores in a sample (i.e., decreasing a sample variance or standard deviation)? Hint: Look at the formulas for the estimated standard error and t-test for a single sample to figure out the answer. A. It will increase the estimated standard error and decrease the likelihood of rejecting H0. B. It will decrease the estimated standard error and decrease the likelihood of rejecting H0. C. It will decrease the estimated standard error and increase the likelihood of rejecting H0. D. It will increase the estimated standard error and increase the likelihood of rejecting H0.

C. It will decrease the estimated standard error and increase the likelihood of rejecting H0.

In a repeated-measures experiment, each individual participates in one treatmentcondition and then moves on to a second treatment condition. One of the majorconcerns in this type of study is that participation in the first treatment mayinfluence the participant's score in the second treatment. How is this problem called? A. Individual differences problem. B. Homogeneity of variance problem. C. Order effect. D. Bi-treatment effect.

C. Order effect.

A hypothesis test with a sample of n = 20 participants produces a t statistic of t = 2.63. Assuming a one-tailed test, what is the correct decision about the outcome of the test? 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 α = .01 but not with α = .05. C. The researcher can reject the null hypothesis with either α = .05 or α = .01. D. The researcher must fail to reject the null hypothesis with either α = .05 or α = .01. E. It is impossible to make the decision without more information.

C. The researcher can reject the null hypothesis with either α = .05 or α = .01.

A sample of n = 15 produces a single sample t statistic of t = - 2.12. If the researcher is using a two-tailed test for hypotheses testing, 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 H0 without more information.

C. The researcher must fail to reject the null hypothesis with either α = .05 or α = .01.

A researcher selects a sample from a population with a mean of μ = 85 and administers a treatment to the individuals in the sample. Which of the following is the correct statement of the null hypothesis for a two-tailed t-test for a single sample? A. μ < 85 B. μ > 85 C. μ = 85 D. M > 85 E. M = 85

C. μ = 85

What is the mean of the t-distribution? A. 10 B. 5 C. 1 D. 0 E. Can't be determined without additional information.

D. 0

The t-test for independent sample can be used to examine ____________. A. The mean difference between two treatment conditions in an experiment (e.g. a difference in performance of experimental group and control group). B. The mean difference between two populations in quasi-experimental designs (e.g., mean difference inattitudes to abortion between residents of the southern vs. northern states in the U.S.). C. The mean difference in stress level at the beginning and the end of semester in a sample of undergraduate students. D. A & B E. All of the above.

D. A & B

Which of the following statements is true about the relationship between the p level, the size of the critical region, and the risk of a Type I error? A. As the p level decreases (e.g., from .05 to .01), the size of the critical region increases, and the risk of a Type I error decreases. B. As the p level decreases (e.g., from .05 to .01), the size of the critical region decreases, and the risk of a Type I error increases. C. As the p level decreases (e.g., from .05 to .01), the size of the critical region increases, and the risk of a Type I error increases. D. As the alpha level decreases (e.g., from .05 to .01), the size of the critical region decreases, and the risk of a Type I error decreases.

D. As the alpha level decreases (e.g., from .05 to .01), the size of the critical region decreases, and the risk of a Type I error decreases.

For which of the following situations would a repeated-measures research design be appropriate? A. Comparing mathematical skills of girls versus boys in elementary school age. B. Comparing verbal skills of science majors versus art majors among undergraduate students C. Comparing self-esteem for students who participate in school athletics versus those who do not. D. Comparing patients' body temperature at the beginning and at the end of medical treatment

D. Comparing patients' body temperature at the beginning and at the end of medical treatment

When n is relatively small (less than 120), how does the shape of the t distribution compare to the normal distribution? A. It is almost perfectly normal. B. It is taller and narrower than the normal distribution. C. There is no consistent relationship between the t distribution and the normal distribution. D. It is flatter and more spread out than the normal distribution.

D. It is flatter and more spread out than the normal distribution.

If other factors are held constant, what is the effect of decreasing the sample size? (Hint: Look at the formulas for the estimated standard error and t-test for a single sample to figure out the answer). A. It will decrease the estimated standard error and increase the likelihood of rejecting H0. B. It will increase the estimated standard error and increase the likelihood of rejecting H0. C. It will decrease the estimated standard error and decrease the likelihood of rejecting H0. D. It will increase the estimated standard error and decrease the likelihood of rejecting H0.

D. It will increase the estimated standard error and decrease the likelihood of rejecting H0.

For which of the following situations would a repeated-measures design have themaximum advantage over an independent-measures design? A. When many subjects are available and individual differences are large. B. When many subjects are available and individual differences are small. C. When very few subjects are available and individual differences are small. D. When very few subjects are available and individual differences are large.

D. When very few subjects are available and individual differences are large.

A sample of n = 25 scores produces a t statistic of t = 3.00. Based on this information, what is the effect size evaluated by r2?

D. r2 = 9/33

For a single sample t-test, what is the sample variance s2 and the estimated standard error sM for a sample of n = 9 scores with SS = 72? A. s2 =8 and sM = 3 B. s2 = 9 and sM = 3 C. s2 = 3 and sM = 1 D. s2 = 9 and sM = 1 E. None of the above.

D. s2 = 9 and sM = 1

With α = .01, the two-tailed critical region for a single sample t test using a sample of n = 25 subjects would have boundaries of ______. A. t = ±2.787 B. t = ±2.756 C. t = ±2.462 D. t = ±2.797 E. None of the above.

D. t = ±2.797

If a research report from an experiment investigating the effect of stress on memory states "t(58) = 2.09, p < .05, 2-tails test" then _______________. A. the researcher rejected H0 and found no significant effect of stress on memory. B. the researcher failed to reject H0 and found a significant effect of stress on memory. C. the researcher failed to reject H0 and found no significant effect of stress on memory. D. the researcher rejected H0 and found a significant effect of stress on memory.

D. the researcher rejected H0 and found a significant effect of stress on memory.

Two samples, each with n = 8, produced an independent sample t statistic of t = 2.17. Which of the following the correct decisions for a two-tailed test? A. Fail to reject H0 with α= .05 but reject H0 with α= .01. B. Fail to reject H0 with both, α= .05 and α= .01. C. Reject H0 with both, α= .05 and α= .01. D. Reject H0 with α= .05 but fail to reject with α= .01.

Reject H0 with α= .05 but fail to reject with α= .01.

A researcher obtains t = 2.74 for a repeated-measures study using a sample of n = 6 participants. Based on this t value, what is the correct decision for a two-tailed test? A. Reject the null hypothesis with α = .05 but fail to reject with α = .01. B. Reject the null hypothesis with either α = .05 or α = .01. C. Fail to reject the null hypothesis with either α = .05 or α = .01. D. Fail to reject the null hypothesis with α = .05 but reject with α = .01.

Reject the null hypothesis with α = .05 but fail to reject with α = .01.

Which of the following is an accurate definition of a Type I error? A. Rejecting a true null hypothesis. B. Failing to reject a false null hypothesis. C. Failing to reject a true null hypothesis D. Rejecting a false null hypothesis.

Rejecting a true null hypothesis.

Which of the following is a fundamental difference between the t statistic and a z-score? A. The t statistic uses the sample mean in place of the population mean. B. The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n. C. The t statistic computes the standard error using a sample variability instead of the population variability. D. All of these are differences between t and z statistics.

The t statistic computes the standard error using a sample variability instead of the population variability.