Question

STAT 2023 Assignment 8 Fall 2019 due by 10pm on Monday, October 21 Estimation of the Population Mean, Lesson 13 Whitmore Farms sells theAmeraucana hens who lay light blue eggs. A random sample of 64 of these hens produced a mean standing height of 14.4 inches. The standard deviation of standing height of Ameraucana hens is known to be .8 inch. Use this information to answer the rest of the questions on this assignment. 1. What is the point estimate for the population mean, the expected height of all Ameraucana hens, based on this sample of 64 hens from whitmorefarm.com? 2. What is the standard error for the point estimate for the mean height of Ameraucana hens? 3. Construct a 90% confidence interval to estimate the mean standing height of Ameraucana hens based on this sample of 64 hens from whitmorefarm.com. 4. Construct a 95% confidence interval to estimate the mean standing height of Ameraucana hens based on this sample of 64 hens from whitmorefarm.com. 5. Construct a 99% confidence interval to estimate the mean standing height of Ameraucana hens based on this sample of 64 hens from whitmorefarm.com. 6. What was the Bound of Error associated with the 90% confidence interval to estimate the mean standing heights of Ameraucana hens that was calculated above? 7. What was the Bound of Error associated with the 95% confidence interval to estimate the mean standing heights of Ameraucana hens that was calculated above? 8. What was the Bound of Error associated with the 99% confidence interval to estimate the mean standing heights of Ameraucana hens that was calculated above? 9. Describe in a sentence the relationship between the bound of error and the width of a confidence interval. 10. Describe in a sentence how increasing the confidence level of the interval estimators affects the width of the intervals. 11. What does it mean to increase the confidence of a confidence interval?

Answer 1

1. What is the point estimate for the population mean, the expected height of all Ameraucana hens, based on this sample of 64 hens from whitmorefarm.com?

Point estimate for the population mean = Sample mean = 14.4 inches

2. What is the standard error for the point estimate for the mean height of Ameraucana hens?

standard error for the point estimate for the mean height = = 0.8 / = 0.1

3. Construct a 90% confidence interval to estimate the mean standing height of Ameraucana hens based on this sample of 64 hens from whitmorefarm.com.

Since population standard deviation is known, we will use z statistic for the confidence interval.

z = 1.645 for 90% confidence interval.

Margin of error = z * Std error = 1.645 * 0.1 = 0.1645

90% confidence interval is,

(14.4 - 0.1645, 14.4 + 0.1645)

(14.2355 , 14.5645)

4. Construct a 95% confidence interval to estimate the mean standing height of Ameraucana hens based on this sample of 64 hens from whitmorefarm.com.

z = 1.96 for 90% confidence interval.

Margin of error = z * Std error = 1.96 * 0.1 = 0.196

95% confidence interval is,

(14.4 - 0.196, 14.4 + 0.196)

(14.204 , 14.596)

5. Construct a 99% confidence interval to estimate the mean standing height of Ameraucana hens based on this sample of 64 hens from whitmorefarm.com.

z = 2.576 for 90% confidence interval.

Margin of error = z * Std error = 2.576 * 0.1 = 0.2576

95% confidence interval is,

(14.4 - 0.2576, 14.4 + 0.2576)

(14.1424 , 14.6576)

6. What was the Bound of Error associated with the 90% confidence interval to estimate the mean standing heights of Ameraucana hens that was calculated above?

Bound of Error = Margin of error = 0.1645

7. What was the Bound of Error associated with the 95% confidence interval to estimate the mean standing heights of Ameraucana hens that was calculated above?

Bound of Error = Margin of error = 0.196

8. What was the Bound of Error associated with the 99% confidence interval to estimate the mean standing heights of Ameraucana hens that was calculated above?

Bound of Error = Margin of error = 0.2576

9. Describe in a sentence the relationship between the bound of error and the width of a confidence interval.

The width of a confidence interval is twice the bound of error.

10. Describe in a sentence how increasing the confidence level of the interval estimators affects the width of the intervals.

The width of a confidence interval increases with the confidence level.

11. What does it mean to increase the confidence of a confidence interval?

Increasing the confidence of a confidence interval is to estimate the population parameter with a higher confidence.