Statistics and Hypothesis - Assignment Example

PART MULTIPLE CHOICE Question The null hypothesis for an independent-measures t test s that the two sample means are equal. Answer True False Question 2 Two separate samples, each with n = 9, will produce an independent-measures t statistic with df = 16. Answer True False Question 3 A researcher reports an independent-measures t statistic with df = 20. Based on the df value, you can conclude that the study used a total of 21 participants. Answer True False Question 4 Cohens d is computed by finding the difference between the two sample means and then dividing by the pooled variance. Answer True False Question 5 If an independent-measures t statistic has df = 20, then there were a total of 22 individuals participating in the research study. Answer True False Question 6 For an independent-measures study with M 1 = 20, M 2 = 16, and a pooled variance of 25, the estimated value for Cohens d = 4/25. Answer True False Question 7 An independent-measures study ____. Answer a. uses a different sample for each of the different treatment conditions being compared b. uses the same sample for each of the different treatment conditions being compared c. uses the data from one sample to evaluate a hypothesis about the population mean d. None of the other choices is correct. Question 8 The alternative hypothesis for an independent-measures t test states: Answer a. There is no mean difference between the two populations being compared. b. There is no mean difference between the two samples being compared. c. There is a non-zero mean difference between the two populations being compared. d. There is a non-zero mean difference between the two samples being compared. Question 9 One sample of n = 10 scores has a variance of s 2 = 6 and a second sample of n = 10 scores has a variance of s 2 = 8. The pooled variance for these two samples will be ____. Answer a. 6 b. 7 c. 8 d. 14 Question 10 In an independent-measures hypothesis test, if t = 0, then ____. Answer a. the two population means must be equal b. the two sample means must be equal c. the two sample variances must be equal d. None of the other choices is correct. Question 11 Which combination of factors is most likely to produce a significant value for an independent-measures t statistic? Answer a. large samples and large variance b. large samples and small variance c. small samples and large variance d. small samples and small variance Question 12 Which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic? Answer a. a small mean difference and small sample variances b. a large mean difference and small sample variances c. a small mean difference and large sample variances d. a large mean difference and large sample variances Question 13 A researcher computes the pooled variance for two samples and obtains a value of 120. If one of the samples has n = 5 scores and the second has n = 10 scores, then what is the value of the estimated standard error for the sample mean difference? Answer a. b. c. d. Question 14 What is the estimated standard error for the independent-measures t statistic for the following two samples? Sample 1: n = 4 with SS = 100. Sample 2: n = 8 with SS = 140. Answer a. 3 b. 9 c. 24 d. 242 Question 15 An independent-measures research study uses two samples, each with n = 12, to compare two treatments. If the results are evaluated with a t statistic using a one-tailed test with α = .01, then the critical region would have a boundary of ____. Answer a. t = 2.797 b. t = 2.492 c. t = 2.819 d. t = 2.508 Question 16 An independent-measures research study uses two samples, each with n = 8 participants. If the data produce a t statistic of t = 2.50, then which of the following is the correct decision for a two-tailed hypothesis test? Answer 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. cannot answer without additional information Question 17 The results of an independent-measures research study are reported as " t(5) = −2.12, p > .05, two tails." What statistical decision was made? Answer a. The researcher failed to reject H 0. b. The null hypothesis was rejected. c. There was a marginally significant effect. d. cannot be determined from the researchers statement Question 18 For an independent-measures t statistic, increasing the number of scores in the sample will ____ measures of effect size, such as Cohens d. Answer a. increase b. decrease c. have little or no effect on d. cannot answer without additional information Question 19 What is required by the homogeneity of variance assumption? Answer a. The two sample variances are equal. b. The two population variances are equal. c. The pooled variance has a value between the two sample variances. d. None of the other options is required by the homogeneity assumption. Question 20 Which of the following research situations would be most likely to use an independent-measures design? Answer a. Examine the development of vocabulary as a group of children mature from age 2 to 3. b. Examine the long-term effectiveness of a stop-smoking treatment by interviewing subjects 2 months and 6 months after the treatment ends. c. Compare the mathematics skills for 9th-grade boys versus 9th-grade girls. d. Compare the blood-pressure readings before medication and after medication for a group of patients with high blood pressure. Question 21 For an independent-measures research study, one sample has M = 20 with s = 22, and the second sample has M = 17 with s = 28. The pooled variance is 25. What is the estimated value of Cohens d for these data? Answer a. d = 3/25 b. d = 3/8 c. d = 3/5 d. The value of d cannot be determined without knowing the sample sizes. PART 2 - SHORT ANSWER QUESTIONS 1.a. The factor influences the numerator of the t statistic and the effect would be to increase the value of t (farther from zero). 1.b. The factor influences the denominator of the t statistic and the effect would be to increase the value of t (farther from zero). 1.c. The factor influences the denominator of the t statistic and the effect would be to decrease the value of t (closer to zero). 2.a. 2.b. 2.c. Critical region: t beyond ±2.228 The test statistic Fail to reject the null hypothesis, . No, this is not enough to reject the null hypothesis for a two-tailed test with α = .05. 2.d. The test statistic is Reject the null hypothesis, . Yes, this is enough to reject the null hypothesis for a two-tailed test with α = .05. 3.a. Step 1: The null and alternate hypotheses are (No difference.) (There is a difference.) Step 2: α = .05 This is an independent measure design. Critical region: t beyond ±2.160 Step 3: The pooled variance is The estimated standard error is The test statistic is Step 4: Reject the null hypothesis, . Yes, there is a significant difference between the attitudes for males and for females. 3.b. About 37.62% of variance accounted for by gender difference. The effect is large. 4. Step 1: The null and alternate hypotheses are (No difference.) (There is a difference.) Step 2: α = .01 This is an independent measure design. Critical region: t beyond ±3.355 Step 3: The data can be summarized as below: Box of Tacks Tacks and Box Separate n 5 5 M 119.2 43.2 SS 2746.8 1066.8 The pooled variance is The estimated standard error is The test statistic is Step 4: Reject the null hypothesis, . Yes, the data indicate a significant difference between the two conditions. Box of Tacks (X - M) (X - M)2 Tacks and Box Separate (X - M) (X - M)2 128 8.8 77.44 42 -1.2 1.44 160 40.8 1664.64 24 -19.2 368.64 113 -6.2 38.44 68 24.8 615.04 101 -18.2 331.24 35 -8.2 67.24 94 -25.2 635.04 47 3.8 14.44 596 SS1 = 2746.8 216 0.00 SS2 = 1066.8 5.a. 30 individuals participated in the entire study. 5.b. Critical region: t beyond ±2.048 Reject the null hypothesis, . Yes, there is a significant difference between the two treatment conditions. 5.c. About 13.27% of variance accounted for by the treatment effect. The effect is medium. 6.a. The null hypothesis is “Housing prices are not going down this year”. 6.b. We would analyze the data with the single-sample t test as the population standard deviation is unknown. We could also use the Z test as the sample size is large (n ≥ 30). 7.a. The null hypothesis is ”Fifth graders do not have more friends than third graders”. (No difference.) or (1-Fifth Grade and 2-Third Grade) 7.b. We would analyze the data with the t test for two independent samples, as there are two independent groups. The study is a quasi-experimental study. 8.a. The null hypothesis is ”If people are made to feel happy, they are not likely to recall more happy childhood events than people who are made to feel sad”. (No difference.) or (1-Happpy and 2-Sad) 8.b. We would analyze the data with the t test for two independent samples, as there are two independent groups. The study is an experimental study. Read More