Question

5) A public bus company official claims that the mean waiting time for bus number 14 during 5) – peak hours is less than 10 minutes. Karen took bus number 14 during peak 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

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 10
Alternative Hypothesis, Ha: μ < 10

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (7.6 - 10)/(2.3/sqrt(18))
t = -4.427

P-value Approach
P-value = 0.0002
As P-value < 0.01, reject the null hypothesis.