Question

A sample of 36 MBA students at a certain university produces a mean age of 26.5 years with a standard deviation of 10.24 years. Which of the following is the 90% confidence interval for the mean age of all MBA students at this university based on this sample.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 26.5

Population standard deviation =    = 10.24
Sample size = n =36

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2    * ( /n)

= 1.645 * ( 10.24 /  36 )

= 2.8075
At 90% confidence interval estimate of the population mean
is,

- E < < + E

26.5 - 2.8075 <   < 26.5+ 2.8075

23.6925<   < 29.3075

( 23.6925, 29.3075)