Question

A simple random sample of 90 items from a population with σ = 7 resulted in a sample mean of 33. If required, round your answers to two decimal places.

a. Provide a 90% confidence interval for the population mean. to

b. Provide a 95% confidence interval for the population mean. to

c. Provide a 99% confidence interval for the population mean.

Answer 1

Solution :

Given that,

a.

Sample size = n = 90

Z/2 = 1.645

Margin of error = E = Z/2* ( /n)

= 1.645 * (7 / 90)

Margin of error = E = 1.21

At 90% confidence interval estimate of the population mean is,

- E < < + E

33 - 1.21 < < 33 + 1.21

A 90% confidence interval for the population mean 31.79 < < 34.21

b.

Sample size = n = 90

Z/2 = 1.96

Margin of error = E = Z/2* ( /n)

= 1.96 * (7 / 90)

Margin of error = E = 1.45

At 95% confidence interval estimate of the population mean is,

- E < < + E

33 + 1.45 < < 33 + 1.45

31.55 < < 34.45

31.55 to 34.45

A 95% confidence interval for the population mean 31.55 to 34.45

c.

Sample size = n = 90

Z/2 = 2.576

Margin of error = E = Z/2* ( /n)

= 2.576 * (7 / 90)

Margin of error = E = 1.90

At 99% confidence interval estimate of the population mean is,

- E < < + E

33 - 1.90 < < 33 + 1.90

31.10 < < 34.90

A 99% confidence interval for the population mean 31.10 to 34.90