Question

Calculate an approximate 95% confidence interval for the population mean salary for engineers, based on the following sample data:

From a sample of 100 engineers, the sample mean salary is $68,000.

Assume the population standard deviation is $4000.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 68000

Population standard deviation = = 4000

Sample size = n = 100

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96 * (4000 / 100)

= 784

At 95% confidence interval estimate of the population mean is,

- E < < + E

68000 - 784 < < 68000 + 784

67216 < < 68784

(67216 , 68784 )