Question

An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the damage may be minor, the company must sell those machines at drastically reduced prices. The company goal is to keep the proportion of damaged machines below 5%. One day an inspector randomly checks 150 washers and finds 6 of them have scratches or dents.

If the true proportion of damaged machines is actually 5.5%, you have made a ___________

Choose one. Type I Error Type II error Correct decision

If the level of significance had been .05, would your answer change? Yes No Choose one.

Answer 1

Ho: p = 0.05

Ha: p < 0.05

Sample proportion = 6/150 = 0.04

Test statistic

z = -0.56

p - Value = P(z < -0.56) = 0.2871

Since this p value is very high, we do not reject Ho and hence, we do not have enough evidence to support that p < 0.05.

We are not rejecting the null hypothesis and the actual proportion is not less than 5% so we have made a correct decision.

If the level of significance had been .05, would your answer change? No