Question

An online catalog company wants on-time delivery for at least 90% of the orders they ship. They have been shipping orders via UPS and FedEx but will switch to a more expensive service (ShipFast) if there is evidence that this service can exceed the 90% on-time goal. As a test the company sends a random sample of orders via ShipFast, and then makes follow-up phone calls to see if these orders arrived on time. Which hypotheses should they test?

Answer 1

H₀: p < 0.90 vs. Hₐ: p ≥ 0.90.

Explanation:

The online catalog company wants at least 90% of the orders they ship to be delivered on-time. If another expensive delivery service can exceed the 90% on-time goal then the company will shift to this service from UPS and FedEx.

So, to determine whether the new shipping service delivers more than 90% orders on-time or not a random sample of orders are shipped via the new shipping service (ShipFast).

A single proportion z-test can be performed to compute the results.

The hypothesis can be defined as:

H₀: The the new shipping service delivers less than 90% orders on-time, i.e. p < 0.90.

Hₐ: The the new shipping service delivers at least 90% orders on-time, i.e. p ≥ 0.90.

The test statistic is:

`z=\frac{\hat p-p}{\sqrt{(p(1-p))/(n)}}`

Decision rule:

If the p-value of the test,
`p-value=P(Z>z)`, is less than the significance level of the test α then the null hypothesis will be rejected. And vice-versa.