In: Statistics and Probability
construct a 99% confidence interval to estimate the population mean using the data below x=36 sigma=9 n=38
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 )