Question

From a sample of 36 graduate​ students, the mean number of months of work experience prior to entering an MBA program was 36.95. The national standard deviation is known to be 19 months. What is a 95​% confidence interval for the population​ mean? A 95​% confidence interval for the population mean is left bracket nothing comma nothing right bracket . ​(Use ascending order. Round to two decimal places as​ needed.)

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 36.95

Population standard deviation =    =19

Sample size n =36

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * ( 19/ 36 )

=6.21
At 95% confidence interval
is,

- E < < + E

36.95 - 6.21 <   < 36.95+ 6.21

(30.74 ,43.16)