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Confidence Intervals for One Proportion Worksheet Math 181 Statistics Helgeson Due at the start of class on Monday, April 1, 2024. Name 1. On the Sections 2.1, 2.2 & 2.3 (Theory-Based Hypothesis Testing for a Single Variable) lecture notes we used simulation and also a theory-based hypothesis test in the first example to determine whether or not we could predict the winner in the California governor's race in November 2010. We found that the p-value was very small and provided very strong evidence against the null hypothesis that the two candidates would each earn 50% of the vote when the actual votes were counted in that election. Using only the exit poll data, Jerry Brown was predicted to be the winner over his opponent Meg Whitman. In that example the exit poll in this gubernatorial race randomly sampled 3889 voters and found that 2065 (or 53.1%) of those voters said they voted for Brown ($\hat{p} = \frac{2065}{3889} = 0.531$). We also checked the validity conditions and found they were all met and we could use a theory-based approach. (a) Now that we know about confidence intervals, construct a 95% confidence interval using the 2SD approach that will estimate the percentage of all voters in that election who vote for Brown. Interpret the result in context. (b) Since the validity conditions are met, construct a 95% confidence interval using the $\hat{p} \pm \text{multiplier} \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ formula. Show your work and interpret the result in context.

          Confidence Intervals for One Proportion Worksheet
Math 181 Statistics
Helgeson
Due at the start of class on Monday, April 1, 2024.
Name
1. On the Sections 2.1, 2.2 & 2.3 (Theory-Based Hypothesis Testing for a Single Variable) lecture notes
we used simulation and also a theory-based hypothesis test in the first example to determine whether or
not we could predict the winner in the California governor's race in November 2010. We found that the
p-value was very small and provided very strong evidence against the null hypothesis that the two
candidates would each earn 50% of the vote when the actual votes were counted in that election. Using
only the exit poll data, Jerry Brown was predicted to be the winner over his opponent Meg Whitman.
In that example the exit poll in this gubernatorial race randomly sampled 3889 voters and found that
2065 (or 53.1%) of those voters said they voted for Brown ($\hat{p} = \frac{2065}{3889} = 0.531$). We also checked the
validity conditions and found they were all met and we could use a theory-based approach.
(a) Now that we know about confidence intervals, construct a 95% confidence interval using the
2SD approach that will estimate the percentage of all voters in that election who vote for Brown.
Interpret the result in context.
(b) Since the validity conditions are met, construct a 95% confidence interval using the
$\hat{p} \pm \text{multiplier} \cdot \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ formula. Show your work and interpret the result in context.

$Confidence Intervals for One Proportion Worksheet Math 181 Statistics Helgeson Due at the start of class on Monday, April 1, 2024. Name 1. On the Sections 2.1, 2.2 2.3 (Theory-Based Hypothesis Testing for a Single Variable) lecture notes we used simulation and also a theory-based hypothesis test in the first example to determine whether or not we could predict the winner in the California governor's race in November 2010. We found that the p-value was very small and provided very strong evidence against the null hypothesis that the two candidates would each earn 50% of the vote when the actual votes were counted in that election. Using only the exit poll data, Jerry Brown was predicted to be the winner over his opponent Meg Whitman. In that example the exit poll in this gubernatorial race randomly sampled 3889 voters and found that 2065 (or 53.1%) of those voters said they voted for Brown ($\hat{p} = \frac{2065}{3889} = 0.531$). We also checked the validity conditions and found they were all met and we could use a theory-based approach. (a) Now that we know about confidence intervals, construct a 95% confidence interval using the 2SD approach that will estimate the percentage of all voters in that election who vote for Brown. Interpret the result in context. (b) Since the validity conditions are met, construct a 95% confidence interval using the p̂±multiplier·√((p̂(1-p̂))/(n)) formula. Show your work and interpret the result in context.$

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