Question

Salaries of 38 college graduates who took a statistics course in college have a? mean, x overbar ?, of $ 61 comma 500 . Assuming a standard? deviation, sigma ?, of ?$11 comma 382 ?, construct a 90 ?% confidence interval for estimating the population mean mu. (Round to the nearest integer as? needed.)

Answer 1

Solution :

Given that,

= 61,500

= 11,382

n = 38

At 90% confidence level the z is ,

  = 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (11,382 / 38) = 3,040

At 90% confidence interval estimate of the population mean is,

- E < < + E

61,500 - 3,040 < < 61,500 - 3,040

58,500 < < 64,500

(58,500 , 64.500)