Question

A random sample of 250 students at a university finds that these students take a mean of 14.3 credit hours per quarter with a standard deviation of 1.5 credit hours. Estimate the mean credit hours taken by a student each quarter using a 98​% confidence interval.

Answer 1

Solution :

Given that,

Point estimate = sample mean = =14.3

Population standard deviation =    = 1.5

Sample size = n =250

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

Margin of error = E = Z/2    * ( /n)

= 2.326 * ( 1.5 /  250 )

= 0.2207
At 98% confidence interval estimate of the population mean
is,

- E < < + E

14.3 - 0.2207 <   < 14.3+ 0.2207

14.0793 <   < 14.5207

( 14.0793 ,14.5207 )