Question

Keep the Highest: 4/12 Attempts: 4 4 Hypothesis tests about a population proportion Aa A firm's carporate stratngy is drtiven largely by ts top maragement team.One methad of gauging the infuence of marketing on caporate stratagy isto measure the pro pertion of firms with a chief marketing officeron their tmp maragement team. Over the 5-year pariad from 2000 to 2004, 42% of firms had a chief marketing officeron their top maragement team. [ Source: Pravin Nath and vijay Mahsjan, "Chief Marketing officers: A Study of Their Presence in Firms Top Manspement Teams,"Jumal af arketing, 70 (2007). Totest the hypoths that the infuence of marketing on caporate stratngy today sdffierent from ts inuence inthe 2000-2004 pariad, a random sampleof B1 US. firms is selected. Ofthese, 32 firms have achief marketing officer on their top maragemant team. The test is canducted at asigrificance level of a-05 Let p be the true proportion of firms wth a chief marketing officer currenty on their top management team. To con the hypothess test, the nul and atemative hypothees are formulated as p D42; H,: p< D42 O Hp-0.42; H,:p D42 O Hp D42; H, p> D42 O -042; H,:p 0.42 the nal hypothes is trum, the sampling distribution of the sample proportion p can be approdmated by a and a standard dleviation of with a mean The test statistic is Sa lct Dibuct Distributions Use the Distributions tool to develop the rejection regian. Acmnding to the rejection regian approach (with a -05), when do you reject the nul hypothesis O Rejact Hgz s -1.645 or Fza 1.645 O Rejact Hgts -1.990 or E ta 1.990 O Reject Hz s -1.960 O REject Hgzs-1.950 or za 1.950 Use the provided Distributions tool to determine the p-value. The p-value is Using the nejection regian apprcach, the nultypothess is , because using the p-value approach, the nul hypothesis is candude that the infuence of marketing on carporate stratngy today bcause Therefare, you s different from ts infuence in the 2000-2004 periad

Answer 1

The detailed solution is given below.

The following information is provided: The sample size is N 81, the number of favorable cases is X 32, and the sample proportion is p 320.3951, and the significance level is a 0.05 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho p 0.42 Ha 0.42 This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used (2) Rejection Region Based on the information provided, the significance level is a 0.05, and the critical value for a two- tailed test is ze = 1.96 The rejection region for this two-tailed test is R {z : \z| > 1.96 (3) Test Statistics The z-statistic is computed as follows: 0.3951 0.42 0.455 V0.42(1 0.42)/81 Vpo(1 - po)/ n (4) Decision about the null hypothesis Since it is observed that z 0.455< ze 1.96, it is then concluded that the null hypothesis is not rejected Using the P-value approach: The p-value is p 0.6493, and since p 0.6493 0.05, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hyppothesis Ho is not rejected. Therefore, there is not enough evidence to 0.05 significance level. claim that the population proportion p is different than po, at the a

If the null hypothesis is true, the sampling distribution of the sample proportion p can be appropimated by a normal distribution with mean 0.42 and a standard deviation of 0.05483

The test statistic is −0.455

Reject Ho if z <= 1.96 or if z >= 1.96

The pvalue = 0.6493

Using the rejection approach the null hypothesis is failed to reject because the
z critical is less than 1.96

Using the pvalue approach the null hypothesis is not rejected because the pvalue is greater then 0.05.