Question

In: Statistics and Probability

construct a 99% confidence interval to estimate the population mean using the data below x=36 sigma=9...

construct a 99% confidence interval to estimate the population mean using the data below x=36 sigma=9 n=38

Solutions

Expert Solution

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 )


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