Question

ANALYZE/INTERPRET THE STUDY AS WELL AS YOUR CONCLUSIONS FROM YOUR CALCULATIONS

DVR’s allow us to skip commercials when watching TV. Some also allow advertisers to see which ads are actually watched. Advertising research indicates that an ad has to be viewed by more than 5% of households to be cost effective (at the very least break even) in the long run. A sample of 250 homes in Cincinnati were monitored to determine viewers’ reactions to a fast food commercial that featured a well-known band. The data revealed 20 of the homes actually viewed the ad

On the basis of this study, will the ad be cost effective for the company? Use the 0.01 significance level.

Answer 1

Solution:

Given:

Sample size = n = 250

x =  of the homes actually viewed the ad = 20

Thus sample proportion of the homes actually viewed the ad is:

Advertising research indicates that an ad has to be viewed by more than 5% of households to be cost effective (at the very least break even) in the long run.

Thus population proportion = p = 0.05

We have to study, if ad will be cost effective for the company.

That is we have to test: if an ad has to be viewed by more than 5% of households to be cost effective.

Thus we use following steps:

Step 1) State H0 and H1:

H0: p = 0.05 Vs H1: p > 0.05

Step 2) Find z test statistic value:

Step 3) Find z critical value:

Level of significance =

Since H1: p > 0.05, which indicates this is right tailed test.

Thus find An Area  

Thus look in z table for Area = 0.9900 or its closest area and find corresponding z critical value.

Area 0.9901 is closest to 0.9900 , thus corresponding z value is 2.3 and 0.03

Thus Z_critical = 2.33

Step 4) Decision Rule:

Reject null hypothesis H0 if z test statistic value > z critical value , otherwise we fail to reject H0.

Since z test statistic value = 2.18 < Z_critical = 2.33 , we fail to reject H0.

Step 5) Conclusion:

Since we failed to reject H0, that is we retain null hypothesis H0: p = 0.05

Thus there is not sufficient evidence to conclude that: ad viewed by more than 5% of households.

Thus on the basis of this study, the ad will not be cost effective for the company