Question

Suppose a pickup and delivery company states that their packages arrive within two days or less on average. You want to find out whether the actual average delivery time is longer than this. You conduct a hypothesis test.

(a) Set up the null and alternative hypotheses.

(b) Suppose you conclude wrongly that the company's statement about average delivery time is within two days. What type of error is being committed and what is the impact of that error?

(c) Suppose you conclude wrongly that the delivery company's average time to delivery is in fact longer than two days. What type of error did you commit and what is the impact of this error?  

(d) Which error is worse from the company's standpoint, a Type I or a Type II error? Why?

(e) Which error is worse from a consumer standpoint, a Type I or a Type II error? Why?

Answer 1

a. Null Hypotheses H₀= 2 days

Alternative Hypotheses H₁= more than 2 days

b. This is Type II error. It is a missed opportunity to say the company's claim about average delivery time is within two days is wrong. The impact of this error is that the consumers will not receive the delivery of their package within 2 days on average and would become disatisfied.

c. In this case we rejected the company's claim about average delivery time of 2 days, but we should not have done so. Thus it is a Type I error. It will cause a false alarm. The impact of this error is that the company will lose its credibility unnecesarrily.

d. From the company's standpoint, Type I error is worse, as the company will lose its reputation unfairly.

e. From the consumer's standpoint, Type II error is Worse, as they will not get their package delivered within the average time promised.