Question

Hypothesis Testing for Population Means When the Population Standard Deviation is NOT known.

Use the t-distribution tables

A pizza delivery chain advertises that it will deliver your pizza in no more than 20 minutes from when the order is placed. Being a skeptic, you decide to test and see if the mean delivery time is actually more than 20 minutes. For the simple random sample of 7 customers who record the amount of time it takes for each of their pizzas to be delivered, the mean is 22.7 minutes with a standard deviation of 4.3 minutes. Perform a hypothesis test using a 0.05 level of significance.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 20
Alternative Hypothesis, Ha: μ > 20

Rejection Region
This is right tailed test, for α = 0.05 and df = 6
Critical value of t is 1.943.
Hence reject H0 if t > 1.943

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (22.7 - 20)/(4.3/sqrt(7))
t = 1.661

P-value Approach
P-value = 0.0739
As P-value >= 0.05, fail to reject null hypothesis.