Question

50.

{Exercise 8.2 (Algorithmic)}

A simple random sample of 90 items from a population with σ = 7 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.
- to -

Answer 1

Solution :

Given that,

σ = 7

= 31

Sample size = n = 90

a)

Z/2 = 1.645

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

= 1.645 * (7 / 90)

= 1.21

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

- E < < + E

31 - 1.21 < < 31 +1.21

29.79 < < 32.21

(29.79, 32.21)

b)

Z/2 = 1.96

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

= 1.96 * (7 / 90)

= 1.42

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

- E < < + E

31 - 1.42 < < 31 +1.42

29.58 < < 32.42

(29.58, 32.42)

c)

Z/2 = 2.576

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

= 2.576 * (7 / 90)

= 1.90

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

- E < < + E

31 - 1.90 < < 31 +1.90

29.10 < < 32.90

(29.10, 32.90)