Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. 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 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.

Answer 1

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

Rejection Region
This is left tailed test, for α = 0.01 and df = 17
Critical value of t is -2.567.
Hence reject H0 if t < -2.567

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.

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