Question

A study was designed to compare two energy drink commercials. Each participant was shown the commercials, A and B, in random order and asked to select the better one. There were 150 women and 140 men who participated in the study. Commercial A was selected by 71 women and by 87 men.

Answer 1

Complete question:

A study was designed to compare two energy drink commercials. Each participant was shown the commercials, A and B, in random order and asked to select the better one. There were 150 women and 140 men who participated in the study. Commercial A was selected by 71 women and by 87 men. Find the odds of selecting Commercial A for the men. Do the same for the women.

Concept:

Logistic Regression: Odds

Given:

Total number of women, n(W) = 150

Total number of men, n(M) = 140

Number of women who selected Commercial A, $n(W_A)$ = 71

Number of men who selected Commercial A, $n(M_A)$ = 87

∴ Number of women who selected Commercial B, $n(W_B)$ = n(W) - $n(W_A)$

                                                                                   = 150 - 71 = 79

Number of men who selected Commercial B, $n(M_B)$ = n(M) - $n(M_A)$

                                                                                   = 140 - 87= 53

Solution:

Proportion of men who chose Commercial A, p = $\frac{n(M_A)}{n(M)}$

                                    p = 87/140

                                    p = 0.62143

Odds of selecting Commercial A for the men = $\frac{p}{1 - p}$

                                                                           $= \frac{0.62143}{1 - 0.62143} \\\\= \frac{0.62143}{0.37857} \\\\= 1.6415$

Proportion of women who chose Commercial A, q = $\frac{n(W_A)}{n(W)}$

                                    q = 71/150

                                    q = 0.47333

Odds of selecting Commercial A for the women = $\frac{q}{1 - q}$

                                                                           $= \frac{0.47333}{1 - 0.47333} \\\\= \frac{0.47333}{0.52667} \\\\= 0.89872$

Hence, the odds of selecting Commercial A for the men are 1.6415 and that for the women are 0.89872.

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