Question

The marketing department for a computer company must determine the selling price for a new model of personal computer. In order to make a reasonable profit, the company would like the computer to sell for $3200. If more than 30% of the potential customers would be willing to pay this price, the company will adopt it. A survey of potential customers is to be carried out; it will include a question asking the maximum amount that the respondent would be willing to pay for a computer with the features of the new model. Let p denote the proportion of all potential customers who would be willing to pay $3200 or more. Then the hypotheses to be tested are Ho: p = .3 versus Ha : p > .3. In the context of this example, describe type I and type II errors. Discuss the possible consequences of each type of error.

Answer 1

H0:Null Hypothesis: p = .3 (Not more than 30% of the potential customers would be willing to pay this price,)

H0:Alternative Hypothesis: p > .3 (More than 30% of the potential customers would be willing to pay this price,) (Claim)

Type I Error: Rejection of a true null hypothesis. Suppose in reality Not more than 30% of the potential customers would be willing to pay this price. But the company wrongly concludes that More than 30% of the potential customers would be willing to pay this price. Type I Error is committed in this situation.

The consequence of Type I Error is that the company will wrongly conclude that more than 30% of the potential customers would be willing to pay this price and the company will adopt it whereas in reality it is not so.

Type II Error: Failure to reject a false null hypothesis. Suppose in reality more than 30% of the potential customers would be willing to pay this price. But the company wrongly concludes that not more than 30% of the potential customers would be willing to pay this price. Type II Error is committed in this situation.

The consequence of Type II Error is that the company will wrongly conclude that not more than 30% of the potential customers would be willing to pay this price and the company will not adopt it whereas in reality it is not so.