MATLAB: An Introduction with Applications
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Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Sampling Distribution of Proportion**
Suppose the true proportion of voters in the county who support a restaurant tax is 0.37. Consider the sampling distribution for the proportion of supporters with a sample size \( n = 108 \).
**Questions:**
1. What is the mean of this distribution?
- [Input box for answer]
2. What is the standard error of this distribution?
- [Input box for answer]
**Explanation:**
- **Mean of the Distribution:** The mean of a sampling distribution of a sample proportion (\( \hat{p} \)) is equal to the true proportion of the population (\( p \)). Thus, the mean is 0.37.
- **Standard Error of the Distribution:** The standard error (SE) can be calculated using the formula:
\[
SE = \sqrt{\frac{p(1-p)}{n}}
\]
where \( p = 0.37 \) and \( n = 108 \).
This exercise helps in understanding the concept of sampling distributions and how they relate to estimating population parameters.](https://content.bartleby.com/qna-images/question/7616b8df-b3d1-40c5-906d-daf9a84f77db/c5cc7cb6-ab79-4d56-a24b-e079390d6cc2/e9i8q1m_processed.jpeg)
Transcribed Image Text:**Sampling Distribution of Proportion**
Suppose the true proportion of voters in the county who support a restaurant tax is 0.37. Consider the sampling distribution for the proportion of supporters with a sample size \( n = 108 \).
**Questions:**
1. What is the mean of this distribution?
- [Input box for answer]
2. What is the standard error of this distribution?
- [Input box for answer]
**Explanation:**
- **Mean of the Distribution:** The mean of a sampling distribution of a sample proportion (\( \hat{p} \)) is equal to the true proportion of the population (\( p \)). Thus, the mean is 0.37.
- **Standard Error of the Distribution:** The standard error (SE) can be calculated using the formula:
\[
SE = \sqrt{\frac{p(1-p)}{n}}
\]
where \( p = 0.37 \) and \( n = 108 \).
This exercise helps in understanding the concept of sampling distributions and how they relate to estimating population parameters.
![According to a 2009 Reader's Digest article, people throw away about 9% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 132 grocery shoppers to investigate their behavior. What is the probability that the sample proportion does not exceed 0.08?
**Note:** You should carefully round any z-values you calculate to 4 decimal places to match WAMAP's approach and calculations.
**Answer =** [_____] (Enter your answer as a number accurate to 4 decimal places.)](https://content.bartleby.com/qna-images/question/7616b8df-b3d1-40c5-906d-daf9a84f77db/c5cc7cb6-ab79-4d56-a24b-e079390d6cc2/t3n000r_processed.jpeg)
Transcribed Image Text:According to a 2009 Reader's Digest article, people throw away about 9% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 132 grocery shoppers to investigate their behavior. What is the probability that the sample proportion does not exceed 0.08?
**Note:** You should carefully round any z-values you calculate to 4 decimal places to match WAMAP's approach and calculations.
**Answer =** [_____] (Enter your answer as a number accurate to 4 decimal places.)
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