Question

You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 24.
Find the critical value that corresponds to a confidence level of 99.9%.
(Report answer accurate to three decimal places with appropriate rounding.)
t_a/2 = ±±

B.Express the confidence interval 43.8±143.843.8±143.8 in the form of a trilinear inequality.

_____<μ<______

C.Assume that a sample is used to estimate a population proportion μμ. Find the margin of error M.E. that corresponds to a sample of size 414 with a mean of 21.2 and a standard deviation of 9.7 at a confidence level of 99.9%.

Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

D.Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 41 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 7.7 and a standard deviation of 3.9. What is the 99% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

_____<μ < _____

Answer 1

(A) The critical value that is use to estimate the population mean with a confidence interval for a confidence level of 99.9% is given as-

For 99.9% confidence level,

____________________________________

(B) The given confidence interval in trilinear inequality is given as-

Hence the confidence interval is

____________________________________

(C) The margin of error(ME) is given by -

where, sample standard deviation, sample size

For 99.9% confidence level,

Given:

                                                    

                                                     

So, the Margin of error(ME) is calculated as ME=1.6

________________________________________________

(D) We need to construct a 99% confidence interval for the true mean number of chocolate chips per cookie for Big Chip cookies.

Given: sample mean , sample standard deviation, sample size

Critical value: For 99% confidence interval,

The confidence interval is calculated as-

                                             

                                             

                                             

                                             

So, the 99% confidence interval for the true mean number of chocolate chips per cookie for Big Chip cookies is calculated as (6.1, 9.3), i.e.,