An employment agency wants to see which of three types of ads in the help-wanted

Question

An employment agency wants to see which of three types of ads in the help-wanted section of local newspapers is the most effective. Three types of ads (big headlines, straightforward, and bold print) were randomly alternated over a period of weeks, and the number of people responding to the ads was noted each week.

Do these data support the null hypothesis that there is no difference in the effectiveness of the ads, as measured by the mean number responding, at the .01 level of significance?

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(b) Find the critical value. (Give your answer correct to two decimal places.)

(c) State the appropriate conclusion.

Type of Advertisement Big Headline Straightforward Bold Print Number of responses (replicates) 27 18 31 23 20 29 37 30 43 48 20 35 26 22 31 23 30

Explanation / Answer

H0: There is no difference in the effectiveness of the ads,

i.e. Means of all groups are equal

Ha: There is difference between the groups

Two tailed hypohtesis test.

We can use chi square test for this

Prepare contingency table

As groups 2 contains less entries, for chi square table we fill up the last blank with mean so that the test will not be affected.

Hence let us use 22 for the blank and do chi square

chi-square = 7.78
degrees of freedom = 10
probability = 0.651

As p value >0.01, we accept null hypohtesis.

Conclusion:

There is no  difference in the effectiveness of the ads

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