The Scenario The Georgia state legislature is considering running their upcoming Senate runoff as a vote by mail only election. The legislators have asked the Election board to commission a study to determine, with 90% confidence, what percentage of voters will support a vote by mail only election. The Election board surveys a sample of Georgia voters. They survey 2086 registered voters, 1266 of which responded to the survey. Of the respondents, 993 said they would support a vote by mail only election. Part A Compute the confidence interval for the sample at a 90% confidence level and provide all your computations. You
The Scenario
The Georgia state legislature is considering running their upcoming Senate runoff as a vote by mail only election. The legislators have asked the Election board to commission a study to determine, with 90% confidence, what percentage of voters will support a vote by mail only election. The Election board surveys a sample of Georgia voters.
They survey 2086 registered voters, 1266 of which responded to the survey. Of the respondents, 993 said they would support a vote by mail only election.
Part A
Compute the confidence interval for the sample at a 90% confidence level and provide all your computations. You may use an app to do the computations. Provide a screenshot of any app you use and all computation you do. Use your confidence interval to answer the follow:
1. What is p-hat? Please give your answer exact to three decimal places.
2. What is the standard error for this interval? Please give your answer exact to four decimal places.
3. What is the confidence interval? Please give your answer in proper interval format exact to four decimal places.
4. Put your interval into context of the scenario.
Part B
After receiving the results of the study, the state legislature decides to do a vote by mail only election and issues a press release stating that 76% registered voters said they would support a vote by mail only election. A local advocacy group is concerned about voter fraud or suppression and disagrees with the conclusion of the state legislature. It claims that the support from voters is not equal to 76%
Conduct a hypothesis test at a 90% confidence level (alpha= 0.1) to test the claim made by the local advocacy group. You may use an app to do the test, if you wish. Include all work and screenshots of any app used. Use the results of your hypothesis test to answer the following questions.
a) What are your null and alternative hypotheses? Be sure to use appropriate notation and justify your choice of the alternative hypothesis from the context of the problem.
b) What is the p-value of your test?
c) What is the conclusion of your hypothesis test? Include statistical justification for your conclusion.
D) Does the hypothesis test support the claim of the local advocacy group? Why or why not?
Part C
Compare the results from the confidence interval and the hypothesis test
Are your results from your confidence interval and hypothesis test consistent? In other words, do both types of inference tests support the same conclusion? Explain why or why not.
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