Answer to Question #327617 in Statistics and Probability for John

Question

A university conducted a tracer study to track its graduates for the past five years. One of the variables included in the study questionnaire asks for data on the monthly salaries of the graduates. A sample of 90 graduates yielded a sample mean equal to Php37 000. Construct a 90% confidence interval for the population mean monthly salary if it is known that the population standard deviation is Php9 470. Interpret the result (Write the interpretation in your solution).

A. 37,000 < μ < 39,000

B. 35,350.01 < μ < 38,640.08

C. 35,357.92 < μ < 38,642.08

D. 37,742.92 < μ < 39,875.01

Answer 1

$CI=\mu \plusmn z\frac{\sigma}{\sqrt{n}}$

z for 90% is 1.645

$CI=37000 \plusmn 1.645\frac{9470}{\sqrt{90}}=37000 \plusmn 1642$

c. $35357.92<\mu<38642.08$