Solution :
Given that,
Point estimate = sample mean =
= 36
Population standard deviation =
= 9
Sample size = n = 38
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2
= Z0.005 = 2.576
Margin of error = E = Z/2*
(
/n)
= 2.576 * (9 /
38)
= 3.76
At 99% confidence interval estimate of
the population mean is,
- E <
<
+ E
36 - 3.76 <
< 36 + 3.76
32.24<
< 39.76
(32.24 , 39.76 )