Question

At Burger Queen outlet it took 40 minutes for a customer to place an order and receive the meal. The Company decided to restructure its operations. The manager would like to find out if the mean time taken in the new system is different from 40 minutes. A
sample of 38 orders showed that it took, on average, 37 minutes to complete the orders with a standard deviation of 7 minutes.

Find the p-value for the test that the mean order completion time is different from 40 minutes.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 40
Alternative Hypothesis: μ ≠ 40

Rejection Region
This is two tailed test, for α = 0.05 and df = 37
Critical value of t are -2.026 and 2.026.
Hence reject H0 if t < -2.026 or t > 2.026

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (37 - 40)/(7/sqrt(38))
t = -2.642

P-value Approach
P-value = 0.0120
As P-value < 0.05, reject the null hypothesis.

Here, significance level is not given so , i consider 0.05