Question

A random sample of 84 items is taken, producing a sample mean of 43. The population standard deviation is 5.89. Construct a 90% confidence interval to estimate the population mean.

Answer 1

( , )

Solution :

Given that,

Point estimate = sample mean = = 43
Population standard deviation =    = 5.89
Sample size = n =84

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2    * ( /n)

= 1.645 * ( 5.89 /   84)

= 1.057
At 90% confidence interval estimate of the population mean
is,

- E < < + E

43 - 1.057 <   < 43 + 1.057

41.943 <   < 44.057