Respuesta :
Answer:
H₀: p < 0.90 vs. Hₐ: p ≥ 0.90.
Step-by-step 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:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
Decision rule:
If the p-value of the test, [tex]p-value=P(Z>z)[/tex], is less than the significance level of the test α then the null hypothesis will be rejected. And vice-versa.
