Question

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 0.84 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 3.06 milligrams. ​

(b) The sample mean is 26 milligrams. Using the minimum sample size with a 95​% level of​ confidence, does it seem likely that the population mean could be within 4​% of the sample​ mean? within 0.4​% of the sample​ mean? Explain.

Answer 1

Answer:

a)

Given,

Here at 95% CI, z value = 1.96

sample size n = (z*s/E)^2

= (1.96*3.06/0.84)^2

= 50.9796

n = 51

b)

CI = xbar +/- z*s/sqrt(n)

= 26 +/- 1.96*3.01/sqrt(51)

= 26 +/- 0.826

= (25.174 26.826)

The 95% confidence interval is (26.174 , 26.826) It is not seem likely that the population mean could be within 4% of the sample mean because 4% off from the sample mean would fall out of CI it's not seem likely that the population mean could be within 0.4% of the sample mean because 0.4% off from the sample mean would fall out of the confidence interval.