Question

In: Statistics and Probability

You may need to use the appropriate appendix table or technology to answer this question. A...

You may need to use the appropriate appendix table or technology to answer this 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

Solutions

Expert Solution

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 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

A 95% confidence interval for the population mean 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 35.09 to 40.91


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