Question

Starting salaries of 140 college graduates who have taken a statistics course have a mean of $43,910. The population standard deviation is known to be $10,625. Using 99% confidence, find both of the following:

A. The margin of error:

B. Confidence interval: , .

Answer 1

Solution :

Given that,

= 43190

= 10625

n = 140

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (10625 / 140) = ( 2313 to more digits ) = 2310

B ) At 99% confidence interval estimate of the population mean is,

- E < < + E

43910 - 2310 < < 43910 + 2310

41600 < < 46200

(41600, 46200 )