Develop a 95 percent confidence interval for the population mean. Interpret the result.

Question

The Greater Pittsburgh Area Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of 15 workers reveals the following number of minutes spent traveling.

29 38 38 33 38 21 45 34 40 37 37 42 30 29 35

a.

Develop a 95 percent confidence interval for the population mean. Interpret the result.

Answer 1

95% CI = x_bar +/- Z*(s/sqrt(n)), and x_bar is sample mean (), n is sample size (15) , Z* is critical value (for 95% confidence level, Z* = 1.96) and s is sample standard deviation ( )

so we have ( - 1.96*/sqrt (15), + 1.96*/sqrt (15) )

=(32.0214, 38.1119)

Interpretation: We are 95% confident that the mean time workers who are employed in the downtown area spend getting to work is between 32.0214 and 38.1119.