Question

50 employees of a company are selected at random and asked how far they commute to work each day. The mean distance (in miles) of 50 employees of a company is 27.9 miles and the standard deviation of the 50 commute distances is 11.5 miles. Use a single value to estimate the mean distance traveled by an employee from that company. Also, find the 95% confidence interval.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 27.9

Population standard deviation =     =11.5

Sample size n =50

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z / 2   = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z / 2     * ( /n)
= 1.96 * ( 11.5 / 50 )

= 3.1876
At 95% confidence interval estimate of the population mean
is,

- E <   < + E

27.9- 3.1876 <   < 27.9 + 3.1876

24.7124 <   < 31.0876

( 24.7124 , 31.0876 )