POL251_HW6(1)

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University of Mississippi *

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Political Science

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Dec 6, 2023

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POL 251: Introduction to Political Science Research Methods Homework #6 Due Thursday, November 16 @ 2:30pm (upload to the BlackBoard assignment, write all partner names on document) Question 1: Imagine a researcher wanted to know if the suicide rate (defined as the number of deaths due to intentional self-harm per 100,000 population) differed between Southern states (ex: Alabama, Florida, Georgia) and non-Southern states. The sample include N=16 Southern states, and N=35 non-Southern states. The average suicide rate for Southern states is 14.7 and the average suicide rate for non-Southern states is 15.8. There is no population information about the standard deviation, but the researchers know that the sample standard deviations are s=2.4 for Southern states, and s=4.4 for non-Southern states. Based upon this information, test the hypothesis that Southern states have a different suicide rate than non- Southern states. (1) Is the proposed hypothesis directional or non-directional ? Does it require a one-tailed or two-tailed statistical test? (2) If you wanted to create confidence intervals around the sample mean for Southern and non-Southern states, would you use the standard normal ( Z ) distribution, or the student’s t distribution? Briefly explain your answer. (3) Use the appropriate lookup table (Z or t based on your answer to part 2), to find the critical value with α = 0.05. Use either a one-tailed or two-tailed test as appropriate based upon your answer to part 1. Write down that critical value and show your work if appropriate. (Hint: If you choose the t statistic, be sure to use use the appropriate degrees of freedom to find the critical value.) (4) Calculate each of the standard errors for Southern and non-Southern states’ samples. You should calculate two different SE’s – one for Southern states, and one for non-Southern states. Use scrap paper to show your work, and round answers to two decimal places. (Hint: SE = s / √ n ) (5) Calculate each of the 95% confidence interval for Southern and non-Southern states’ samples. You should calculate two different CI’s – one for Southern states, and one for non-Southern states. Use scrap paper to show your work, and round answers to two decimal places. (Hint: C.I. = µ +/- Z*SE for the standard normal distribution; C.I. = µ +/- t*SE for the t-distribution). (6) Based on your calculated 95% confidence intervals, do Southern states have a different suicide rate than non-Southern states? Briefly explain why or why not. 1
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