3. Whitmore Farms sells the Ameraucana hens who lay light blue eggs. A random sa

Question

3. Whitmore Farms sells the Ameraucana 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. a. What is the point estimate for the population mean, the expected height of all b. What is the standard error for the point estimate for the mean height of C. Construct a 90% confidence interval to estimate the mean standing height of d. Construct a 95% confidence interval to estimate the mean standing height of e. Construct a 99% confidence interval to estimate the mean standing height of f. What was the Bound of Error associated with the 90% confidence interval to Ameraucana hens, based on this sample of 64 hens from whitmorefarm.com? Ameraucana hens? Ameraucana hens based on this sample of 64 hens from whitmorefarm.com. Ameraucana hens based on this sample of 64 hens from whitmorefarm.com. Ameraucana hens based on this sample 64 hens from whitmorefarm.com. estimate the mean standing heights of Ameraucana hens that was calculated above? g. 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? 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? h. i. Describe in a sentence the relationship between the bound of error and the . Describe in a sentence how increasing the confidence level of the interval k. What does it mean to increase the confidence of a confidence interval? width of a confidence interval estimators affects the width of the intervals

Explanation / Answer

SolutionA:

point estimate for population mean=samplemean=14.4

Solutionb:

standard error=stddeviation/sqrt(sample szie)

=0.8/sqrt(64)

=0.8/8

=0.1

std erooror=0.1

Solutionc:

90% confidence inetrval for population mean=

sample mean-zcrit(stddeviation/sqrt(samplesize),sample mea+zcrit(stddeviation/sqrt(samplesize)

z crit for 90%=1.645

therfore,

14.4-1.645(0.8/sqrt(64),14.4+1.645(0.8/sqrt(64)

14.24,14.56

we are 90% confident that the true population mean height lies in between

14.24 and 14.56 inches

Solutiond:

Z crit for 95%=1.96

95% confidence interval for true population mean is

14.4-1.96(0.8/sqrt(64),14.4+1.96(0.8/sqrt(64)

14.20,14.59

lower limit=14.2

upper limit=14.59

we are 95% confident that the true population mean lies in between

14.2 and 14.59 inches

  

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