Question

A particular book publisher is thinking about starting up a new national magazine in a small town. It's thought that this publisher would have to get over 12% of the book market to be financially secure. While planning to launch this magazine, a survey was taken of a sample of 400 readers. After providing an inside look into this magazine, one question asked the participants if they would subscribe to this magazine if the cost didn't exceed $20 per month. Suppose that the number of participants that said they would subscribe is 58.

a. Can this publisher conclude that this proposed magazine will be financially feasible?

b. Suppose that the true value of the overall proportion of readers who will subscribe to this magazine is .13. Was the decision made in part a correct? If not, what type of error was made?

c. State the meaning of a type 1 and type 2 error in the content of this example. What would be the consequences of making these errors to the publisher?

Answer 1

Ans:

a)assume alpha=0.05

Test statistic:

z=(0.145-0.12)/SQRT(0.12*(1-0.12)/400)

z=1.539

critical z value=1.645

Fail to reject the null hypothesis.

There is not sufficient evidence to conclude that this proposed magazine will be financially feasible.

b)Type II error was made,as we fail to reject the null hypothesis and null hypothesis is false,

c)Type I error is to conclude that overall proportion of readers who will subscribe to this magazine is over 0.12 ,but in fact it is less than or equal to 0.12

Type II error is to conclude that overall proportion of readers who will subscribe to this magazine is less than or equal to 0.12 ,but in fact it is over 0.12.

if we make made type I error means that project was not financially feasible and we launched the magazine,so he will be in loss.if we make made type II error means that project was financially feasible and we did not launched the magazine,so we missed opportunity.