Question

# An online retailer ships products from overseas with an advertised delivery date within 10 days. To...

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

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

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