10. You are doing a research project in political science to determine the proportion of voters in your district who favor capital punishment. a. If no preliminary sample of voters is taken to estimate p, how large a sample is necessary to be 99% sure that the point estimate will be within a distance of .01 from p? b. The NORC found that approximately 67% of people in the U.S. favor capital punishment. How large a sample is necessary to be 99% sure that the point estimate will be within a distance of .01 from p?

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# Sample Size Determination in Political Science Research

## Problem 10

You are conducting a research project in political science to determine the proportion of voters in your district who favor capital punishment.

### Part a
If no preliminary sample of voters is taken to estimate \( p \), how large a sample is necessary to be 99% sure that the point estimate will be within a distance of 0.01 from \( p \)?

### Part b
The NORC found that approximately 67% of people in the U.S. favor capital punishment. How large a sample is necessary to be 99% sure that the point estimate will be within a distance of 0.01 from \( p \)?

---

## Questions 11 - 12

### Part a
What is the null hypothesis? What is the alternate hypothesis?

### Part b
What is the level of significance? What is the critical value \( z_0 \) (#12)?

### Part c
Calculate the \( t \) or \( z \) (round \( \hat{p} \) to 4 places) values corresponding to the sample statistic.

### Part d
Find the \( P \) value.

### Part e
Based on your answer, reject or fail to reject the null hypothesis?
Transcribed Image Text:# Sample Size Determination in Political Science Research ## Problem 10 You are conducting a research project in political science to determine the proportion of voters in your district who favor capital punishment. ### Part a If no preliminary sample of voters is taken to estimate \( p \), how large a sample is necessary to be 99% sure that the point estimate will be within a distance of 0.01 from \( p \)? ### Part b The NORC found that approximately 67% of people in the U.S. favor capital punishment. How large a sample is necessary to be 99% sure that the point estimate will be within a distance of 0.01 from \( p \)? --- ## Questions 11 - 12 ### Part a What is the null hypothesis? What is the alternate hypothesis? ### Part b What is the level of significance? What is the critical value \( z_0 \) (#12)? ### Part c Calculate the \( t \) or \( z \) (round \( \hat{p} \) to 4 places) values corresponding to the sample statistic. ### Part d Find the \( P \) value. ### Part e Based on your answer, reject or fail to reject the null hypothesis?
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