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)	38	20	34
	46	23	32
	39	27	31
	42	28	32
	32	22	45
	25		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.)
1

(b) Find the critical value. (Give your answer correct to two decimal places.)
2

Answer 1

a)

Big Headline Straightforward Bold Print Senior X3 X3 Total 95 105 102 104 102 X2 20 32 31 32 45 38 4 27 42 32 2 2 Total-2X - Average-X-2X/n- Total-EX2- S (x(X)2/n)/(n-1)- Total observation number of grou 212 35.3333 7634 28.67 573 24.0000 2926 11.50 grand meanXrand24.9130 37.0000 8494 56.00 3.1667 1.37 17 pS between groups degree of freedom dfbg-k-1 - within groups degree of freedom dfw -N-k = Total degree of freedom 2 df 16 Tota Big Headline Straightforward Bold Print 37.0000 24.0000 35.3333 56.000 11.500 28.667 280.00 46.00 143.33 30.7843469.3333 116.78 368.79 45.21 total sum of square between groups SSG- 2(n-1) S SSG+SSE- 530.7843 469.3333 1000.1176 sum of square within groups SSE total sum of square SST = Summary table Source of variation Between groups with in groups total df MS 265.39 33.52 7.92 530.78 469.33 1000.12 2 16

from above test statistic F=7.92

b)

for (2,16) degree of freedom and 0.01 level crtiical value F=6.51