Question

A random sample of ?n measurements was selected from a population with standard deviation ?=11.7 and unknown mean ?. Calculate a 95% confidence interval for ? for each of the following situations:

(a) ?=60, ?=85
≤?≤

(b)  ?=75, ?=85
≤?≤

(c)  ?=100, ?=85
≤?≤

Answer 1

Solution :

Given that,

(a)

Sample size = n = 60

Z/2 = 1.96

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

= 1.96 * (11.7 / 60)

Margin of error = E = 3.0

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

- E + E

85 - 3.0 85 + 3.0

82 88

(b)

Sample size = n = 75

Z/2 = 1.96

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

= 1.96 * (11.7 / 75)

Margin of error = E = 2.6

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

- E + E

85 - 2.6 85 + 2.6

82.4 87.6

(c)

Sample size = n = 100

Z/2 = 1.96

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

= 1.96 * (11.7 / 100)

Margin of error = E = 2.3

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

- E + E

85 - 2.3 85 + 2.3

82.7 87.3