Question

A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus number 14 during peek hours on 18 different occasions. Her mean waiting time was 7.6 minutes with a standard deviation of 2.3 minutes. At the 0.01 significance level, test the claim that the mean waiting time is less than 10 minutes. Use the P-value method of testing hypotheses.

Answer 1

Solution:

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 10

Ha: 10

The test statistics,

t =( - )/ (s /n)

= ( 7.6 - 10 ) / ( 2.3 / 18 )

= -4.427

P-value = 0.0002

The p-value is p = 0.0002 < 0.01, it is concluded that the null hypothesis is rejected.

There is sufficient evidence to claim that the mean waiting time is less than 10 minutes.