Question

y was designed to compare two energy drink commercials. Each shown the commercials in random order and asked to select the better participant was ommercial A was selected by 45 out of 100 women and 80 out of 140 men. sure to check the necessary conditions. with 0.08 precision and 96% confidence, what sample size would you a. Is there evidence that commercial preferences are different between genders? Be o. If it is desirable to estimate the proportion of women who prefer Commercial B recommend?

Answer 1

Given that Compare two energy drink commercials. commercial A was selected by 45 at 100 women and 80 out of 140 men. If evidence that commercial preference are different b/w genders. Data: - sample size of women (n_1) = 100 No, of women selected (x_1) = 45 Sample proportion of women (p^^_1) = 45/100 = 0.45 Sample size of men (n_2) = 140 No. of men selected (x_2) = 80 Sample proportion of men (p^^_2) = 80/140 = 0.571 combined proportion (p^^) = x^1 + x^2/n^1 + n^2 = 45 + 80/100 + 140 p^^= 0.5208 (1 - p^^) = 0.4792 H_0: p_1 = p_2 verses H_a: p_1 notequalto p_2 test statistic 2 = p^^_1 - p^^2/ squareroot p^^(1 - p^^) (1/n, + 1/n_2) = (0.450 - 0.571)/squareroot 05208 times 0.4792 times (1/100 + 1/140) z = - 0.121/0.06541 = 1.8498 P - value = 0.0322 times 2 = 0.0644. > 0.05 at 5% and 1% level of significance