Question

A simple random sample of 60 items from a population with

σ = 5

resulted in a sample mean of 31.

(a)

Provide a 90% confidence interval for the population mean.

(b)

Provide a 95% confidence interval for the population mean.

(c)

Provide a 99% confidence interval for the population mean.

Answer 1

a) .

90% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

31 - 1.645 * 5 / sqrt(60) < < 31 + 1.645 * 5 / sqrt(60)

29.94 < < 32.06

90% CI is ( 29.94 , 32.06)

b)

95% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

31 - 1.96 * 5 / sqrt(60) < < 31 + 1.96 * 5 / sqrt(60)

29.73 < < 32.27

95% CI is ( 29.73 , 32.27)

c)

99% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

31 - 2.576 * 5 / sqrt(60) < < 31 + 2.576 * 5 / sqrt(60)

29.34 < < 32.66

99% CI is ( 29.34 , 32.66)