Question

A simple random sample of 70 items from a population with σ = 8 resulted in a sample mean of 31.

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

standard dev.= σ = 8

mean = u = 31

n = 70

a.  90% confidence interval for the population mean = u (+/-) Z _90% * σ / n

Z _90% = 1.64

U = 31 + 1.64 * 8 / 70 = 31 + 1.57 = 32.57

L = 31 - 1.64 * 8 / 70 = 31 - 1.57 = 29.43

CI => ( 29.43 , 32.57 )

b.  95% confidence interval for the population mean = u (+/-) Z _95% * σ / n

Z _95% = 1.96

U = 31 + 1.96 * 8 / 70 = 31 + 1.88 = 32.88

L = 31 - 1.96 * 8 / 70 = 31 - 1.88 = 29.12

CI => ( 29.12 , 32.88 )

c.  99% confidence interval for the population mean = u (+/-) Z _99% * σ / n

Z _99% = 2.57

U = 31 + 2.57 * 8 / 70 = 31 + 2.47 = 33.47

L = 31 - 2.57 * 8 / 70 = 31 - 2.47 = 28.53

CI => ( 28.53 , 33.47 )