Question

 

A simple random sample with

n = 56

provided a sample mean of 26.5 and a sample standard deviation of 4.4. (Round your answers to one decimal place.)

(a)

Develop a 90% confidence interval for the population mean.

to

(b)

Develop a 95% confidence interval for the population mean.

to

(c)

Develop a 99% confidence interval for the population mean.

to

(d)

What happens to the margin of error and the confidence interval as the confidence level is increased?

As the confidence level increases, there is a smaller margin of error and a more narrow confidence interval.As the confidence level increases, there is a larger margin of error and a wider confidence interval.    As the confidence level increases, there is a smaller margin of error and a wider confidence interval.As the confidence level increases, there is a larger margin of error and a more narrow confidence interval.

Answer 1

The confidence interval for population mean based on the sample mean is

Here  n = 56, sample mean of and a sample standard deviation of

a) A 90% confidence interval ()for the population mean is

b) A 95% confidence interval ()for the population mean is

c) A 99% confidence interval ()for the population mean is

d) Margin of error is proportional to the width of the CI.

So we see

"As the confidence level increases, there is a larger margin of error and a wider confidence interval".