Question

A random sample of 130 observations produced a mean of ?⎯⎯⎯=36.1x¯=36.1 from a population with a normal distribution and a standard deviation σ=4.87.

(a) Find a 95% confidence interval for μ
≤ μ ≤

(b) Find a 99% confidence interval for μ
≤ μ ≤

(c) Find a 90% confidence interval for μ
≤ μ ≤

Answer 1

Solution :

Given that,

(a)

Sample size = n = 130

Z_/2 = 1.96

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

= 1.96 * (4.87 / 130)

= 0.8

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

- E + E

36.1 - 0.8 36.1 + 0.8

35.3 36.9

(b)

Sample size = n = 130

Z_/2 = 2.576

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

= 2.576 * (4.87 / 130)

= 1.1

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

- E + E

36.1 - 1.1    36.1 + 1.1

35.0 37.2

(c)

Sample size = n = 130

Z_/2 = 1.645

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

= 1.645 * (4.87 / 130)

= 0.7

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

- E + E

36.1 - 0.7 36.1 + 0.7

35.4 36.8