eBook The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = 0.17 and a simple random sample of 800 households will be selected from the population. Use z-table. a. Calculate the sampling distribution of p, the proportion of households spending more than $100 per week on groceries. E(F) = (to 2 decimals) oF = (to 4 decimals) b. What is the probability that the sample proportion will be within +0.02 of the population proportion (to 4 decimals)? C. What is the probability that the sample proportion will be within ±0.02 of the population proportion for a sample of 1600 households (to 4 decimals)?

MATLAB: An Introduction with Applications
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**Exercise 07.37**

The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is \( p = 0.17 \) and a simple random sample of 800 households will be selected from the population. Use the z-table.

a. Calculate the sampling distribution of \(\bar{p}\), the proportion of households spending more than $100 per week on groceries.

- \( E(\bar{p}) = \) _____ (to 2 decimals)
- \( \sigma_{\bar{p}} = \) _____ (to 4 decimals)

b. What is the probability that the sample proportion will be within ±0.02 of the population proportion (to 4 decimals)?

c. What is the probability that the sample proportion will be within ±0.02 of the population proportion for a sample of 1600 households (to 4 decimals)?

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**Question 8 of 8**
Transcribed Image Text:**Exercise 07.37** The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is \( p = 0.17 \) and a simple random sample of 800 households will be selected from the population. Use the z-table. a. Calculate the sampling distribution of \(\bar{p}\), the proportion of households spending more than $100 per week on groceries. - \( E(\bar{p}) = \) _____ (to 2 decimals) - \( \sigma_{\bar{p}} = \) _____ (to 4 decimals) b. What is the probability that the sample proportion will be within ±0.02 of the population proportion (to 4 decimals)? c. What is the probability that the sample proportion will be within ±0.02 of the population proportion for a sample of 1600 households (to 4 decimals)? [**Icon Key**] - Save - Submit Assignment for Grading - Check My Work **Question 8 of 8**
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