Answer to Question #214091 in Statistics and Probability for Madimetja

Question

A new bus route has been established between downtown Pretoria North and Montana. Pandu has taken the bus to work for many years. For the old bus route, she knows from long experience that the mean waiting time between buses at her stop was 20 minutes. However, a random sample of five waiting times between buses using the new route had a mean of 15:1 minutes with sample standard deviation of 6:2 minutes. Does this indicate that the population mean waiting time for the new route is shorter than what it used to be? Test the hypothesis using D 0:05. Assume that X; the waiting time is normally distributed. Write down the hypothesis to be tested and show all the steps and calculations.

Answer 1

$H_0: \mu=20 \\ H_1: \mu <20$

Degree of freedom (df) = 4

$\bar{x}=15.1 \\ s=6.2$

t-statistic

$t = \frac{\bar{x}-\mu}{d/ \sqrt{n}} \\ t=\frac{15.1-20}{6.2/ \sqrt{5}}=-1.76$

α=0.05

df=4

$t_{crit}= -2.13$

Reject H₀ if $t<t_{crit}$

Thus, -1.76> -2.13

Fail to reject H₀.

We cannot conclude that the population mean waiting time for the new route is shorter than what it used to be.