Answer ### Estimating Mean Cholesterol Content in Cheese ServingsA cheese processing company aims to estimate the mean cholesterol content of all one-ounce servings of a specific type of cheese. The estimate must be within 0.79 milligrams of the population mean.#### Problem Statement1. **Determine the Sample Size:** - **Objective:** Determine the minimum sample size required to construct a 95% confidence interval for the population mean, assuming the population standard deviation is 3.11 milligrams. - **Solution:** - The minimum sample size required to construct a 95% confidence interval is calculated as \( 71 \) servings. - **Note:** This value is rounded up to the nearest whole number.2. **Assess Population Mean Relative to the Sample Mean:** - **Objective:** Given a sample mean of 32 milligrams and using the minimum sample size with a 95% confidence level, determine whether it seems likely that the population mean could be within 3% of the sample mean or within 0.3% of the sample mean. Provide an explanation based on the confidence interval. - **Solution:** - The 95% confidence interval is \( \left[ 31.21, 32.79 \right] \). - **Within 3% of Sample Mean:** - It **seems likely** that the population mean could be within 3% of the sample mean because the interval formed by the values 3% away from the sample mean **entirely contains** the confidence interval. - **Within 0.3% of Sample Mean:** - It **does not seem** likely that the population mean could be within 0.3% of the sample mean because the interval formed by the values 0.3% away from the sample mean **overlaps but does not entirely contain** the confidence interval. - **Note:** Round values to two decimal places as needed.#### Useful References:- [Standard Normal Table: Page 1](#)- [Standard Normal Table: Page 2](#)This detailed analysis provides a methodological approach for estimating the mean cholesterol content in cheese servings, ensuring accuracy and confidence in the results.

A cheese processing company wants to estimate the mean cholesterol content of all one-ounce servings of a type of cheese. The estimate must be within 0.79 milligram of the population mean. (a) Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 3.11 milligrams. (b) The sample mean is 32 milligrams. Using the minimum sample size with a 95% level of confidence, does it seem likely that the population mean could be within 3% of the sample mean? within 0.3% of the sample mean? Explain. Click here to view page 1 of the Standard Normal Table. Click here view page 2 of the Standard Normal Table.

A cheese processing company wants to estimate the mean cholesterol content of all one-ounce servings of a type of cheese. The estimate must be within 0.79 milligram of the population mean. (a) Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 3.11 milligrams. (b) The sample mean is 32 milligrams. Using the minimum sample size with a 95% level of confidence, does it seem likely that the population mean could be within 3% of the sample mean? within 0.3% of the sample mean? Explain. Click here to view page 1 of the Standard Normal Table. Click here view page 2 of the Standard Normal Table.

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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### Estimating Mean Cholesterol Content in Cheese Servings

A cheese processing company aims to estimate the mean cholesterol content of all one-ounce servings of a specific type of cheese. The estimate must be within 0.79 milligrams of the population mean.

#### Problem Statement

1. **Determine the Sample Size:**
- **Objective:** Determine the minimum sample size required to construct a 95% confidence interval for the population mean, assuming the population standard deviation is 3.11 milligrams.

- **Solution:**
- The minimum sample size required to construct a 95% confidence interval is calculated as \( 71 \) servings.
- **Note:** This value is rounded up to the nearest whole number.

2. **Assess Population Mean Relative to the Sample Mean:**
- **Objective:** Given a sample mean of 32 milligrams and using the minimum sample size with a 95% confidence level, determine whether it seems likely that the population mean could be within 3% of the sample mean or within 0.3% of the sample mean. Provide an explanation based on the confidence interval.

- **Solution:**
- The 95% confidence interval is \( \left[ 31.21, 32.79 \right] \).

- **Within 3% of Sample Mean:**
- It **seems likely** that the population mean could be within 3% of the sample mean because the interval formed by the values 3% away from the sample mean **entirely contains** the confidence interval.

- **Within 0.3% of Sample Mean:**
- It **does not seem** likely that the population mean could be within 0.3% of the sample mean because the interval formed by the values 0.3% away from the sample mean **overlaps but does not entirely contain** the confidence interval.
- **Note:** Round values to two decimal places as needed.

#### Useful References:
- [Standard Normal Table: Page 1](#)
- [Standard Normal Table: Page 2](#)

This detailed analysis provides a methodological approach for estimating the mean cholesterol content in cheese servings, ensuring accuracy and confidence in the results.

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