For each of the following situations, state whether a Type I, a Type II, or neither error has been made. Explain brief ly.

a) A company wants to determine whether more than 70%

of its customers are satisfied with its front desk services.

They test H0: p = 0.7 vs. HA: 7 0.7, and reject the null hypothesis. Later, they find out that 66% of all their customers are satisfied with the front desk services.

b) A sample of 250 residents from a residential area was selected and were asked to participate in a survey regarding their preference of shopping online or off line. The result shows no evidence that preference for online shopping is not 0.5. Later, all the residents in the residential area are tested, and no difference is found.

c) Many runners usually complete a 5km run within an average time of 33 minutes. A sample of 103 runners’ run time during a recent 5km running competition was recorded, and an average run time of 32.5 minutes was determined. The result shows fail to reject the null hypothesis with the mean of 33 minutes. Finally, when all the runners of the race had been considered, it gave a mean run time of 31.9 minutes.

d) A manufacture claims that only 2% of their productions are defective. A test has been conducted which found a P-value of 0.0865 that shows fail to reject the null hypothesis.

Further testing shows that the manufacturer actually has 1.6% defective productions.