Question

An online retailer ships products from overseas with an advertised delivery date within 10 days. To test whether or not deliveries are made within the advertised time, a random sample of

n= 15 orders is selected. The sample mean delivery time is 12 days, and the sample standard deviation is 3 days. Does the evidence suggest that the mean delivery time is actually more than 10 days using a level of significance at 0.05?

COMPLETE the 5-step process for solving tests of hypotheses

Answer 1

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

Rejection Region
This is right tailed test, for α = 0.05 and df = 14
Critical value of t is 1.761.
Hence reject H0 if t > 1.761

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (12 - 10)/(3/sqrt(15))
t = 2.582

P-value Approach
P-value = 0.0109
As P-value < 0.05, reject the null hypothesis.

There is sufficient evidence to conclude that the  the evidence suggest that the mean delivery time is actually more than 10