Question

A random sample of ? measurements was selected from a population with standard deviation ?=13.7 and unknown mean ?. Calculate a 99 % confidence interval for ? for each of the following situations:

(a) n=55, x¯=100.4
≤?≤

(b)  n=75, x¯=100.4
≤?≤

(c)  n=105, x¯=100.4
≤?≤

Answer 1

Solution :

Given that,

(a)

Sample size = n = 55

Z/2 = 2.576

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

= 2.576 * (13.7 / 55)

Margin of error = E = 4.8

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

- E + E

100.4 - 4.8 100.4 + 4.8

95.6 105.2

(b)

Sample size = n = 75

Z/2 = 2.576

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

= 2.576 * (13.7 / 75)

Margin of error = E = 4.1

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

- E + E

100.4 - 4.1 100.4 + 4.1

96.3 104.5

(c)

Sample size = n = 105

Z/2 = 2.576

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

= 2.576 * (13.7 / 105)

Margin of error = E = 3.4

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

- E + E

100.4 - 3.4 100.4 + 3.4

97.0 103.8