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.

	Type of Advertisement
	Big Headline	Straightforward	Bold Print
Number of responses (replicates)	39	28	36
	48	28	44
	24	29	40
	33	29	35
	31	25	39
	33		38

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.)

Answer 1

We use the one way ANOVA with replication tool of Excel and get the following ANOVA table SUMMARY Groups Count Sum Average Variance Big Headline Straightforward Bold Print 6 208 34.6667 65.8667 2.7 6 232 38.6667 10.2667 5 139 27.8 ANOVA Source of VariationSS Between Groups Within Groups df MS P-value F crit 325.4745 391.4667 14 27.9619 2 162.7373 5.8200 0.0145 6.5149 Total 716.9412 16 a) As from the table above, we can see the test statistic is F 5.82 b) Critical value of F is obtained from F-tables or Excel function F.INV.RT using degrees of freedom 2 and 14 and level of significance 0.01 F-crit F.INV.RT(0.01, 2, 14) F-crit 6.51 6.51 Conclusion Since Ftest statistic < F-crit, we do not reject the null hypothesis Thus the data supports 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