Question

A random sample of ? measurements was selected from a population with standard deviation ?=16.6 and unknown mean ?. Calculate a 90 % confidence interval for ? for each of the following situations: (a) ?=65, ?⎯⎯⎯=86.1 (b) ?=80, ?⎯⎯⎯=86.1 (c) ?=100, ?⎯⎯⎯=86.1

Answer 1

Solution :

Given that,

(a)

Sample size = n = 65

Z_/2 = 1.645

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

= 1.645 * (16.6 / 65)

= 3.4

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

- E < < + E

86.1- 3.4< < 86.1+ 3.4

82.7 < < 89.5

(82.7 , 89.5)

(b)

Sample size = n = 80

Z_/2 = 1.645

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

= 1.645 * (16.6 / 80)

= 3.1

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

- E < < + E

86.1 - 3.1 < < 86.1 + 3.1

83.0 < < 89.2

(83.0 , 89.2)

(c)

Sample size = n = 100

Z_/2 = 1.645

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

= 1.645 * (16.6 / 100)

= 2.7

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

- E < < + E

86.1 - 2.7 < < 86.1 + 2.7

83.4< < 88.8

(83.4 , 88.8)