Question

A major home improvement store conducted its biggest brand recognition campaign in the company’s history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who “like the ads a lot”. A study of 1,189 adults who viewed the ads 230 indicated that they “like the ads a lot.” The percentage of a typical television advertisement receiving the “like the ads a lot” score is believed to be 22%. Company officials want to know if there is evidence that the series of television advertisements are as successful as the typical ad at a 0.01 level of significance.

a. Re-test the above hypothesis using the p-value and the 0.02 level of significance.

b. In which case are you more likely to have a type II error?

c. What does it mean to make such an error? (In general and in terms of the problem.)

d. What would be the consequences of making a type II error? (Respond in the context of the problem)

Answer 1

a) The null and alternative hypothesis

H0: p= 0.22

Ha; p< 0.22

This is a left tailed test as the alternative hypothesis is p<0.22

Test statistic is

where

n=1189 ,

P value = P( z < -2.21)

From z table , P( z < -2.21) = 0.0135

Thus , P value = 0.0135

If level of significance is

P value > 0.01

We fail to reject H0

At 0.01 level of significance , there is evidence that series of advertisements are as successful as the typical ad.

If level of significance is

P value < 0.02

We reject H0

At 0.02 level of significance , there is evidence that new series of advertisements are not as successful as the typical ad.

b) Type II error is the error of accepting a false null hypothesis

As for , we fail to reject the null hypothesis ( that is we accept the null hypothesis)

If the null hypothesis is false , we accept a wrong null hypothesis

At , we are more likely to have a type II error

c) Type II error is the error of accepting a false null hypothesis

That is if in reality if p=0.22 is wrong , rather p< 0.22 is correct

That is if in reality the new series of advertisements are not as successful as typical ads

But on the basis of the test we conclude the new series of advertisements are as successful as typical ads

As a result the Company spends money on the new Advertisements in vain which are not as popular as the typical ads .

d)The consequences of type II error

On the basis of the test we conclude the new series of advertisements are as successful as typical ads , whereas in reality the new series of advertisements are not as successful as typical ads

As a result the Company spends money on the new advertisements in vain which are not as popular as the typical ads .