Question

newspaper publisher is considering launching a new "national" newspaper in Anytown. It is believed that the newspaper would have to capture over 12% of the market in order to be financially viable. During the planning stages of this newspaper, a market survey was conducted of a sample of 400 readers. After providing a brief description of the proposed newspaper, one question asked if the survey participant would subscribe to the newspaper if the cost did not exceed $20 per month. Suppose that 58 participants said they would subscribe.

a. Can the publisher conclude that the proposed newspaper will be financially viable? Perform the appropriate test at a 1% level of significance.

b. Suppose the actual value of the overall proportion of readers who would subscribe to this newspaper is 0.13. Was the decision made in part (a) correct? If not, what type of error was made?

c. State the meaning of a Type I and Type II error in the context of this scenario. And what would be the repercussions of making these errors to the publisher?

Answer 1

newspaper publisher is considering launching a new "national" newspaper in Anytown. It is believed that the newspaper would have to capture over 12% of the market in order to be financially viable. During the planning stages of this newspaper, a market survey was conducted of a sample of 400 readers. After providing a brief description of the proposed newspaper, one question asked if the survey participant would subscribe to the newspaper if the cost did not exceed $20 per month. Suppose that 58 participants said they would subscribe.

a. Can the publisher conclude that the proposed newspaper will be financially viable? Perform the appropriate test at a 1% level of significance.

Ho: P=0.12, H1: P> 0.12

p=58/400 = 0.145

=1.5386

Table value of z at 0.01 level = 2.326

Rejection Region: Reject Ho if z > 2.326

Calculated z = 1.5386 not in the rejection region

The null hypothesis is not rejected.

There is not enough evidence to conclude that the newspaper captured over 12% of the market.

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.12
Level of Significance	0.01
Number of Items of Interest	58
Sample Size	400
Intermediate Calculations
Sample Proportion	0.145
Standard Error	0.0162
Z Test Statistic	1.5386
Upper-Tail Test
Upper Critical Value	2.3263
p-Value	0.0619
Do not reject the null hypothesis

b. Suppose the actual value of the overall proportion of readers who would subscribe to this newspaper is 0.13. Was the decision made in part (a) correct? If not, what type of error was made?

When the actual proportion is 0.13 which is greater than null hypothesis value 0.12 but we failed to reject the false null hypothesis. We made type II error.

c. State the meaning of a Type I and Type II error in the context of this scenario. And what would be the repercussions of making these errors to the publisher?

Type I is that we conclude that the newspaper captured over 12% of subscribers and actually true subscribers is 12%.

Type II is that we conclude that the newspaper captured 12% of subscribers and actually true subscribers is over 12%.