Question

Expensive ads Consumers who think a product’s advertising is expensive often also think the product must be of high quality. Can other information undermine this effect? To find out, marketing researchers did an experiment. The subjects were 90 women from the clerical and administrative staff of a large organization. All subjects read an ad that described a fictional line of food products called “Five Chiefs.” The ad also described the major TV commercials that would soon be shown, an unusual expense for this type of product. The $45$women who were randomly assigned to the control group read nothing else. The $45$in the “undermine group” also read a news story headlined “No Link between Advertising Spending and New Product Quality.” All the subjects then rated the quality of Five Chefs products on a seven-point scale. The study report said, “The mean quality ratings were significantly lower in the undermine treatment (xA  4.56) than in the control treatment $\left({\overline{x}}_C=5.05;t=2.64,P<0.01\right)$.

(a). Explain why the Random and Independent conditions are met in this case.

(b) The distribution of individual responses is not Normal, because there is only a seven-point scale. Why is it still proper to use a two-sample t-test?

(c) Interpret the P-value in context.

Short answer

a). Independent and random conditions are met.

b). Normal requirement is met.

c). The possibility of the mean difference being predicted as in this or more extreme study is $1\%$.

Step-by-step solution

Part (a) Step 1: Given Information

The mean quality ratings were significantly lower in the undermine treatment $\left({\overline{x}}_A=4.56\right)$ than in the control treatment$\left({\overline{x}}_{\mathrm{C}}=5.05;t=2.64,P<0.01\right)$.

Part (a) Step 2: Explanation

Random: $45$ Women have been randomly assigned to the control group, while the remaining women have been assigned to the undermining group, thereby fulfilling the random criterion.

Independent: Satisfied, as the sample size is smaller than $10\%$ of the population

Part (b) Step 1: Given Information

The mean quality ratings were significantly lower in the undermine treatment $\left({\overline{x}}_A=4.56\right)$than in the control treatment $\left({\overline{x}}_C=5.05;t=2.64,\mathrm{P}<0.01\right)$.

Part (b) Step 2: Explanation

They both have a sample size of $45$. Because both samples have a sample size of at least $30$, it can be concluded that both samples are normally distributed and hence met the usual criterion.

Part (c) Step 1: Given Information

$P<0.01=1\%$.

Part (c)  Step 2: Explanation

$P<0.01=1\%$

This means that since all groups have a mean sample population, the possibility of the mean difference being predicted as in this or more extreme study is$1\%$.