Question

The customer service department of a local gas utility believes that the population mean time between the entry of the service request and the connection of service is always less than 90 days. A random sample of 64 houses from the records available during the past year reveals a sample mean of 99 days and a standard deviation of 20 days. Using a level of significance of 0.01, is there evidence that the population mean waiting time in the past year is greater than 90 days. Please state the null and alternative hypotheses, identify the significance level, critical values, and calculate the test statistics, make a final decision to "reject" or "Do not reject" the null hypothesis, and draw the conclusion. What is the p-value? What does it mean?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 90
Alternative Hypothesis, Ha: μ < 90

Rejection Region
This is left tailed test, for α = 0.01 and df = 63
Critical value of t is -2.387.
Hence reject H0 if t < -2.387

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (99 - 90)/(20/sqrt(64))
t = 3.60

P-value Approach
P-value = 0
As P-value < 0.01, reject the null hypothesis.

There is sufficient evidence to conclude that the population mean waiting time in the past year is greater than 90 days