HW # 3- STUDENT_VERSION

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Feb 20, 2024

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HW # 3 CHP 7 1. A population is normally distributed with a mean of 56 and a standard deviation of 12.If a sample of 36 participants is selected from this population, what is the standard error of the mean (σM)?Answer: ____ 2. A population is normally distributed with a mean of 56 and a standard deviation of 12.Assuming n = 36, what is the likelihood of selecting a sample at random from this population with a sample mean equal to at least M = 60? 3. A population is normally distributed with a mean of 56 and a standard deviation of 12. What is the mean of the sampling distribution (µM) for this population? 4. A population is normally distributed with a mean of 12 and a variance of 256. If a sample of 64 participants is selected from this population, what is the standard error of the mean (σM)? Answer: ____ [enter whole number] 5. A researcher selects two samples of 64 participants each. In the first sample, the population mean was 10 and the variance was 16. In the second sample, the population mean was 25 and the variance was 9. Which sample will be associated with a larger standard error of the mean? a. Sample 1. b. Sample 2. c. Neither; both samples will have the same value for standard error. Population for Sample 1 Population for Sample 2 Mean 10 25 Variance 16 9 St. Dev. 4 3 n 64 64 6. A researcher selects a sample of 169 participants from a population with a mean of 38 and a standard deviation of 26. About 68% of the sample means in this sampling distribution should be between a sample mean of: [Hint: Use the empirical rule to find the best answer] a. 18 and 58. b. 34 and 38. c. 38 and 44 d. 36 and 40. 7. A researcher records data in a population with a mean of 12 and a standard deviation of 9. Suppose the researcher obtains two samples from this population. Sample 1 is n = 50 and Sample 2 is n = 100. Which sample will be associated with a smaller standard error? a. Sample 1. b. Sample 2. c. Neither; both samples will be associated with the same value for standard error. 8. A researcher records data in a population with a mean of 12 and a standard deviation of 9. Suppose the researcher obtains a sample of n = 100, yet after the data is collected, they find that 20 participants must be removed from the sample, leaving n = 80 as the final sample size. What will happen to the standard error as a result of reducing the sample size from 100 to 80 participants? a. The standard error will decrease.

b. The standard error will increase. c. Nothing, the standard error will not change. 9. A researcher selects a sample of 81 participants from a population with a mean of 8 and a standard deviation of 9. About 14% of the sample means in this sampling distribution should be between a sample mean of: [Hint: Use the empirical rule to find the best answer] a. 6 and 8. b. 5 and 6. c. 9 and 10 d. 10 and 11. CHP 8 10. A researcher records a sample of scores on a standardized assessment and compares these scores to the average score nationally of 52 (µ = 52) and a standard deviation of 8 (σ = 8). The score are in the table below. After computing a one-sample z test for these data, what is the value of the z statistic? Answer: ____ scores 50 65 54 53 60 45 50 52 55 60 70 58 11. A researcher records a sample of scores on a standardized assessment and compares these scores to the average score nationally of 52 (µ = 52) and a standard deviation of 8 (σ = 8). The score are in the table below. What is the decision for the one-sample z test using a two-tailed test at a .05 level of significance? scores 50 65 54 53 60 45 50

a. Fail to reject the null hypothesis. b. Reject the null hypothesis. 12. A researcher records the time to complete an attentional assessment and compares these scores to the average score nationally of 110 seconds (µ = 110) and a standard deviation of 10 (σ = 10). After computing a one-sample z test for these data, what is the value of the z statistic? 13. What is the decision for the one-sample z test using a two-tailed test at a .05 level of significance? a. Fail to reject the null hypothesis. b. Reject the null hypothesis. 14. Given the following z statistic: What is the effect size using Cohen’s d? Z obt = !"#!$ ! √#$ 15. State whether the effect size using Cohen’s d is small, medium, or large. Answer S for small, M for medium, and L for large. 16. What is the effect size using Cohen’s d if the sample size is increased to 100? 17. A researcher reports that the size of an effect in some population is d = 0.80. Which of the following is an appropriate interpretation for Cohen’s d? a. There is an 80% likelihood of detecting the significant effect observed in the population. b. 88% of the variability in the dependent variable can be explained by the independent variable. c. Mean scores were significant by 0.80 points in the population. d. Mean scores shifted 0.80 standard deviations in the population. 18. A researcher evaluates scores on a standardized assessment with a known standard deviation of σ = 1.0. Which of the following lists the 95% confidence interval for these data? a. 95% CI 5.00, 5.50 b. 95% CI 4.76, 5.74 52 55 60 70 58 Scores 110 120 115 130 120 118 116 140 90 105 110 115

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c. 95% CI 3.52, 6.48 d. 95% CI 4.84, 5.66 Scores 5 7 4 4 6 5 7 6 5 4 3 5 6 7 6 4

HW # 3- STUDENT_VERSION

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