Corporate advertising tries to enhance the image of the corporation. A study com

Question

Corporate advertising tries to enhance the image of the corporation. A study compared two ads from two sources, the Wall Street Journal and the National Enquirer. Subjects were asked to pretend that their company was considering a major investment in Performax, the fictitious sportswear firm in the ads. Each subject was asked to respond to the question "How trustworthy was the source in the sportswear company ad for Performax?" on a 7-point scale. Higher values indicated more trustworthiness. Here is a summary of the results.

Find the two-sample pooled t statistic. Then formulate the problem as an ANOVA and report the results of this analysis. Verify that F = t 2.

Explanation / Answer

Here the

Pooled standard deviation sp = sqrt [{(n1 -1)s12 + (n2 -1)s22 }/ (n1 + n2-2) ] = sqrt [65 * 1.502 + 60 * 1.642)/(66 + 61-2)]

= 1.5688

standard error of the mean difference se0 = sp * sqrt [1/n1 + 1/n2] = 1.5688 * sqrt [1/66 + 1/61] = 0.2786

test statistic

t = (x1 - x2)/ se0 = (4.77 - 2.43)/0.2786 = 8.3991

Here the ANOVA analysis

The grand mean = xbar = (66 * 4.77 + 61 * 2.43)/127 = 463.05/127 = 3.646

Here Sum of squares for within treatments = SSW = (x - xbar)2 n =  66 * (3.646 - 4.77)2 + 61 * (3.646 - 2.43)2 = 173.5808

Here degree of freedom for within groups = dFW =1

MSW = 173.5808/1 = 173.5808

Sum of square for error = SSE = (n-1)s2 = (66-1)1.502 + (61-1) 1.642 = 307.626

Here degree of freedom for between groups = dFW =125

MSE = 307.626/125 = 2.461

F = MSW/MSE = 173.5808/2.461 = 70.5326

so here we can see that t2 = 8.39912 = 70.544 which is equal to F

so F = t2

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