1. An independent-measures study uses two samples, each with n = 13, to compare two treatment conditions. What is the df value for the t statistic for this study? (1 point) 2. A researcher reports t(24) = 5.30, p < .01 for an independent-measures experiment. How many individuals participated in the entire experiment? (1 point) 3. A researcher reports an independent-measures t statistic with df = 40. If the two samples are the same size (n1 = n2), then how many individuals are in each sample? (1 point) 4. Calculate and describe in words the steps for finding the pooled variance from the below information (3 pts: 1 point for correct answer, 2 points for clear description). Sample 1: n = 10 and S2 = 40 Sample 2: n = 6 and S 2 = 50 5. Why do we need to find the pooled standard error? (2 points) 6. Describe in words the steps for finding the standard error from the information you were given in problem 5. (2 points) 7. An independent-measures study with n = 3 in each sample, produces a sample mean difference of 3 points and a pooled variance of 27. What is the value for the calculated t statistic? (2 points) 8. Two samples, each with n = 12 scores, produce an independent-measures t statistic of t = 3.00. If the effect size is measured using r 2, what is the value of 2? (2 points) 9. For an independent-measures t statistic, what is the effect of decreasing the number of scores in the samples on the critical value of T? (1 point) 10. Which combination of factors in sample size and variance size is most likely to produce a significant value for an independent-measures t statistic? (1 point) 11. Why does changing the degrees of freedom influence the critical value of T (hint, look at the T distribution graphs in your book or slides). (2 points) 12. A researcher conducts an independent-measures study on how serotonin is related to aggression. He believes that serotonin will increase aggression. One sample of rats is a control group and gets a placebo that does not affect serotonin. A second sample of rats gets a drug that lowers serotonin. Then the researcher records the number of aggressive responses each of the rats displays. Here are the data (9 pts total this problem) Control Low Serotonin n rats = 10 n rats = Mean aggressive Mean 11 aggressive displays = 14 displays = 19 S2 = 10 2 S = 14 a. What are the null and alternate hypotheses? (1 point) b. What is the pooled variance? (2 point) c. What is the pooled standard error? (2 point) d. What value of T do you get for your calculation? (2 points) e. If the critical T for a two tailed alpha at .05, is + or - 2.069, can you reject the null hypothesis? (1 point) f. Compute Cohen's D to measure the size of the treatment effect. (1 point) 1. An independent-measures study uses two samples, each with n = 13, to compare two treatment conditions. What is the df value for the t statistic for this study? (1 point) df = n1 + n2 - 2 = 13 + 13 - 2 =24 2. A researcher reports t(24) = 5.30, p < .01 for an independentmeasures experiment. How many individuals participated in the entire experiment? (1 point) The degrees of freedom for the study is 24, df=n-1=24, n=25. 3. A researcher reports an independent-measures t statistic with df = 40. If the two samples are the same size (n1 = n2), then how many individuals are in each sample? (1 point) df=n1+n2-2=40 n1+n2=42 n1=n2=42/2= 21 4. Calculate and describe in words the steps for finding the pooled variance from the below information (3 pts: 1 point for correct answer, 2 points for clear description). Sample 1: n = 10 and S2 = 40 Sample 2: n = 6 and S2 = 50 Pooled Variance= Pooled Variance= ( n11 )s 21 +( n21 )s22 n1 +n2 2 (101 )40+ ( 61 )50 10+62 Pooled Variance=43.57 5. Why do we need to find the pooled standard error? (2 points) When the two group size are the same, pooled standard error equal the usual standard error for the difference in means 6. Describe in words the steps for finding the standard error from the information you were given in problem 5. (2 points) Standard error is the square root of ratio of pooled variance and sum of the reciprocal of sample sizes. So, first we calculate the pooled variance as mentioned in the above question, followed by calculation of the sum of the reciprocal of sample sizes. Then we calculate the ratio of the two, and take the square root of the outcome. 7. An independent-measures study with n = 3 in each sample, produces a sample mean difference of 3 points and a pooled variance of 27. What is the value for the calculated t statistic? (2 points) t statistic = Mean difference / Pooled variance t statistic = 3 / 27 =0.11 8. Two samples, each with n = 12 scores, produce an independentmeasures t statistic of t = 3.00. If the effect size is measured using r2, what is the value of 2? (2 points) 2 ( 3.00) t2 = 2 = = 2 = 9 / 31= 2 t +(n1 +n2 2) (3.00) +(12+122) 2 2 = 0.2903 9. For an independent-measures t statistic, what is the effect of decreasing the number of scores in the samples on the critical value of T? (1 point) For an independent-measures t statistic, as the number of scores in the sample decreases, the critical value of T increases. 10. Which combination of factors in sample size and variance size is most likely to produce a significant value for an independent-measures t statistic? (1 point) A high number of sample size and a low variance size is most likely to produce a significant value for an independent-measures t statistic. 11. Why does changing the degrees of freedom influence the critical value of T (hint, look at the T distribution graphs in your book or slides). (2 points) Because As the degrees of freedom increases, the area in the tails of the t-distribution decreases while the area near the center increases 12. A researcher conducts an independent-measures study on how serotonin is related to aggression. He believes that serotonin will increase aggression. One sample of rats is a control group and gets a placebo that does not affect serotonin. A second sample of rats gets a drug that lowers serotonin. Then the researcher records the number of aggressive responses each of the rats displays. Here are the data (9 pts total this problem) Control Low Serotonin n rats = 10 n rats = 11 Mean aggressive Mean aggressive displays = 14 displays = 19 S2 = 10 S2 = 14 a. What are the null and alternate hypotheses? (1 point) Null Hypothesis: There is no difference in the number of aggressive responses between the two treatments. Alternate Hypothesis: There is a significant difference in the number of aggressive responses between the two treatments. b. What is the pooled variance? (2 point) n1=11 2 s 1=14 n2=10 s 22=10 Pooled Variance= ( n11 )s 21 + ( n21 )s22 n1 +n2 2 Pooled Variance= ( 111 )14 + ( 101 )10 230 = =12.11 11+102 19 Pooled Variance=12.11 c. What is the pooled standard error? (2 point) ( n1 + n1 )= 12.11( 111 + 101 )=1.52 Pooled Standard Error= Pooled Variance 1 2 d. What value of T do you get for your calculation? (2 points) t-value = (Mean1 - Mean2) / Pooled Standard Error t-value = (19 - 14) / 1.52 =3.30 e. If the critical T for a two tailed alpha at .05, is + or - 2.069, can you reject the null hypothesis? (1 point) Since, t-value 30.30 is higher than the critical value, we reject the null hypothesis. f. Compute Cohen's D to measure the size of the treatment effect. (1 point) Cohen's D = (Mean2 - Mean1) / Pooled Standard deviation Cohen's D = (14 - 19) / sqrt(12.11.30) =-1.52 1. An independent-measures study uses two samples, each with n = 13, to compare two treatment conditions. What is the df value for the t statistic for this study? (1 point) df = n1 + n2 - 2 = 13 + 13 - 2 =24 2. A researcher reports t(24) = 5.30, p < .01 for an independentmeasures experiment. How many individuals participated in the entire experiment? (1 point) The degrees of freedom for the study is 24, df=n-1=24, n=25. 3. A researcher reports an independent-measures t statistic with df = 40. If the two samples are the same size (n1 = n2), then how many individuals are in each sample? (1 point) df=n1+n2-2=40 n1+n2=42 n1=n2=42/2= 21 4. Calculate and describe in words the steps for finding the pooled variance from the below information (3 pts: 1 point for correct answer, 2 points for clear description). Sample 1: n = 10 and S2 = 40 Sample 2: n = 6 and S2 = 50 Pooled Variance= Pooled Variance= ( n11 )s 21 +( n21 )s22 n1 +n2 2 (101 )40+ ( 61 )50 10+62 Pooled Variance=43.57 5. Why do we need to find the pooled standard error? (2 points) When the two group size are the same, pooled standard error equal the usual standard error for the difference in means 6. Describe in words the steps for finding the standard error from the information you were given in problem 5. (2 points) Standard error is the square root of ratio of pooled variance and sum of the reciprocal of sample sizes. So, first we calculate the pooled variance as mentioned in the above question, followed by calculation of the sum of the reciprocal of sample sizes. Then we calculate the ratio of the two, and take the square root of the outcome. 7. An independent-measures study with n = 3 in each sample, produces a sample mean difference of 3 points and a pooled variance of 27. What is the value for the calculated t statistic? (2 points) t statistic = Mean difference / Pooled variance t statistic = 3 / 27 =0.11 8. Two samples, each with n = 12 scores, produce an independentmeasures t statistic of t = 3.00. If the effect size is measured using r2, what is the value of 2? (2 points) 2 ( 3.00) t2 = 2 = = 2 = 9 / 31= 2 t +(n1 +n2 2) (3.00) +(12+122) 2 2 = 0.2903 9. For an independent-measures t statistic, what is the effect of decreasing the number of scores in the samples on the critical value of T? (1 point) For an independent-measures t statistic, as the number of scores in the sample decreases, the critical value of T increases. 10. Which combination of factors in sample size and variance size is most likely to produce a significant value for an independent-measures t statistic? (1 point) A high number of sample size and a low variance size is most likely to produce a significant value for an independent-measures t statistic. 11. Why does changing the degrees of freedom influence the critical value of T (hint, look at the T distribution graphs in your book or slides). (2 points) Because As the degrees of freedom increases, the area in the tails of the t-distribution decreases while the area near the center increases 12. A researcher conducts an independent-measures study on how serotonin is related to aggression. He believes that serotonin will increase aggression. One sample of rats is a control group and gets a placebo that does not affect serotonin. A second sample of rats gets a drug that lowers serotonin. Then the researcher records the number of aggressive responses each of the rats displays. Here are the data (9 pts total this problem) Control Low Serotonin n rats = 10 n rats = 11 Mean aggressive Mean aggressive displays = 14 displays = 19 S2 = 10 S2 = 14 a. What are the null and alternate hypotheses? (1 point) Null Hypothesis: There is no difference in the number of aggressive responses between the two treatments. Alternate Hypothesis: There is a significant difference in the number of aggressive responses between the two treatments. b. What is the pooled variance? (2 point) n1=11 2 s 1=14 n2=10 s 22=10 Pooled Variance= ( n11 )s 21 + ( n21 )s22 n1 +n2 2 Pooled Variance= ( 111 )14 + ( 101 )10 230 = =12.11 11+102 19 Pooled Variance=12.11 c. What is the pooled standard error? (2 point) ( n1 + n1 )= 12.11( 111 + 101 )=1.52 Pooled Standard Error= Pooled Variance 1 2 d. What value of T do you get for your calculation? (2 points) t-value = (Mean1 - Mean2) / Pooled Standard Error t-value = (19 - 14) / 1.52 =3.30 e. If the critical T for a two tailed alpha at .05, is + or - 2.069, can you reject the null hypothesis? (1 point) Since, t-value 30.30 is higher than the critical value, we reject the null hypothesis. f. Compute Cohen's D to measure the size of the treatment effect. (1 point) Cohen's D = (Mean2 - Mean1) / Pooled Standard deviation Cohen's D = (14 - 19) / sqrt(12.11.30) =-1.52