Question

A simple random sample of 50 items from a population with

σ = 8

resulted in a sample mean of 38. (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.

to

Answer 1

Solution :

Given that,

(a)

Sample size = n = 50

Z/2 = 1.645

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

= 1.645 * (8 / 50)

Margin of error = E = 1.86

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

- E < < + E

38 - 1.86 < < 38 + 1.86

36.14 < < 39.86

A 90% confidence interval for the population mean is 36.14 to 39.86

(b)

Sample size = n = 50

Z/2 = 1.96

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

= 1.96 * (8 / 50)

Margin of error = E = 2.22

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

- E < < + E

38 - 2.22 < < 38+2.22

35.78 < < 40.22

A95% confidence interval for the population mean is 35.78 to 40.22

(c)

Sample size = n = 50

Z/2 = 2.576

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

= 2.576 * (8 / 50)

Margin of error = E = 2.91

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

- E < < + E

38 - 2.91 < < 38 + 2.91

35.09 < < 40.91

A 99% confidence interval for the population mean is 35.09 to 40.91