Question

Gonzaga University professors conducted a study of television commercials and published their results in the Journal of Sociology, Social Work and Social Welfare (Vol 2, 2008). The key research question was: “Do television advertisers use religious symbolism to sell goods and services?” In a sample of 797 TV commercials collected in 1998, only 16 commercials used religious symbolism. Of the sample of 1,499 TV commercials examined in the more recent study, 51 commercials used religious symbolism.

(a) Construct a 90% confidence interval for the true difference in pro- portions of TV commercials that use religious symbolism between the years 1998 and 2008.

(b) Conduct an analysis to determine if the percentage of TV commercials that use religious symbolism has changed since the 1998 study. Test the hypothesis at a significance level of ? = 0.10.

(c) Compute the p-value for this test.

Answer 1

Given n_1 = 797 x_1 = 16 (1998 study) n_2 = 1499 x_2 = 51 (Recent study) The 90% confidence interval for the true difference proportions of TV commercials that use religious symbolism between the years 1998 and 2008 is (p_1^- p_2^) plusorminus z_alpha/2 squareroot PQ (1/n_1 + 1/n_2), where p_1^= x_1/n_1 = 16/797 = 0.02 , p_2^= x_2/n_2 = 51/1499 = 0.034 p = x_1 + x_2/n_1 + n_2 = 16 + 51/797 + 1499 = 0.0292 , Q = 1 - p = 1 - 0.029 = 0.971 z_alpha/2 = 1.645, is the significant value of z at alpha = 0.10 \r\n (p_1^- p_2^) plusorminus z_alpha/2 squareroot PQ (1/n_1 + 1/n_2) = (0.02 - 0.034) plusorminus 1.645 squareroot 0.029 times 0.971 (1/797 + 1/1499) = -0.014 plusorminus 0.01209 = (- 0.02609, - 0.00191) The null hypothesis is H_): p_1 = p_2 The alternative hypothesis is H_1: p_1 notequalto p_2 The test statistic is z = p_1^- p_2^/squareroot PQ (1/n_1 + 1/n_2) = 0.02 - 0.034/squareroot 0.0292 times 0.971 (1/797 + 1/1499)