Question

Suppose the average bus wait times are normally distributed with an unknown population mean and a population standard deviation of of five minutes. A random sample of 30 bus wait times are taken and has a sample mean of 25 minutes.

Find a 95% confidence interval estimate for the population mean wait time.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 25

Population standard deviation =    = 5

Sample size n =30

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 * (5 / 30)

= 1.79
At 95% confidence interval
is,

- E < < + E

25 - 1.79 <   < 25 + 1.79

23.21 <   < 26.79