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a) If you take a sample of size 59, can we say that the sampling distribution of p is approximately normal? Why or why not? Check conditions (use a cutoff of 5 to make your decision): 1. np = which ? v 2. n(1 - p) = which ? v Can we say that the sampling distribution of p is approximately normal in this case? (If the answer is no, state the first conditions in the list above that failed) Select an answer b) Redo part a assuming p has increased to 45%. (use a cutoff of 5 to make your decision): 1. np = which ? v 2. n(1 - p) = which ? v Can we say that the sampling distribution of p is approximately normal in this case? (If the answer is no, state the first conditions in the list above that failed) Select an answer

a) If you take a sample of size 59, can we say that the sampling distribution of p is approximately normal? Why or why not? Check conditions (use a cutoff of 5 to make your decision): 1. np = which ? v 2. n(1 - p) = which ? v Can we say that the sampling distribution of p is approximately normal in this case? (If the answer is no, state the first conditions in the list above that failed) Select an answer b) Redo part a assuming p has increased to 45%. (use a cutoff of 5 to make your decision): 1. np = which ? v 2. n(1 - p) = which ? v Can we say that the sampling distribution of p is approximately normal in this case? (If the answer is no, state the first conditions in the list above that failed) Select an answer

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Population and Sampling Distribution Task** **Scenario:** You have a population of 28,000 people, where 4% of the population has a particular disease. **Objective:** Determine if the sampling distribution of the sample proportion (\(\hat{p}\)) is approximately normal under different conditions. **Given Data:** - Population (\(N\)): 28,000 - Proportion (\(p\)): 4% **Tasks:** **a) Sample Size of 59:** Determine if the sampling distribution of \(\hat{p}\) is approximately normal. 1. **Check Conditions:** - Calculate \( n \times p \): - \(n = 59\) - \(p = 0.04\) - \( np = \_\_\_ \) - Compare \( np \) to 5. - Calculate \( n(1 - p) \): - \(1 - p = 0.96\) - \( n(1 - p) = \_\_\_ \) - Compare \( n(1 - p) \) to 5. **Conclusion:** Can we say that the sampling distribution of \(\hat{p}\) is approximately normal? - If no, state the condition that failed. **b) Increased Proportion to 45%:** Redo the calculations assuming \( p \) is 45%. 1. **Check Conditions:** - Calculate \( n \times p \): - \(n = 59\) - \(p = 0.45\) - \( np = \_\_\_ \) - Compare \( np \) to 5. - Calculate \( n(1 - p) \): - \(1 - p = 0.55\) - \( n(1 - p) = \_\_\_ \) - Compare \( n(1 - p) \) to 5. **Conclusion:** Can we say that the sampling distribution of \(\hat{p}\) is approximately normal? - If no, state the condition that failed.
Transcribed Image Text:**Population and Sampling Distribution Task** **Scenario:** You have a population of 28,000 people, where 4% of the population has a particular disease. **Objective:** Determine if the sampling distribution of the sample proportion (\(\hat{p}\)) is approximately normal under different conditions. **Given Data:** - Population (\(N\)): 28,000 - Proportion (\(p\)): 4% **Tasks:** **a) Sample Size of 59:** Determine if the sampling distribution of \(\hat{p}\) is approximately normal. 1. **Check Conditions:** - Calculate \( n \times p \): - \(n = 59\) - \(p = 0.04\) - \( np = \_\_\_ \) - Compare \( np \) to 5. - Calculate \( n(1 - p) \): - \(1 - p = 0.96\) - \( n(1 - p) = \_\_\_ \) - Compare \( n(1 - p) \) to 5. **Conclusion:** Can we say that the sampling distribution of \(\hat{p}\) is approximately normal? - If no, state the condition that failed. **b) Increased Proportion to 45%:** Redo the calculations assuming \( p \) is 45%. 1. **Check Conditions:** - Calculate \( n \times p \): - \(n = 59\) - \(p = 0.45\) - \( np = \_\_\_ \) - Compare \( np \) to 5. - Calculate \( n(1 - p) \): - \(1 - p = 0.55\) - \( n(1 - p) = \_\_\_ \) - Compare \( n(1 - p) \) to 5. **Conclusion:** Can we say that the sampling distribution of \(\hat{p}\) is approximately normal? - If no, state the condition that failed.
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