The executives of CareFree Insurance, Inc.feel that "a majority of our employees perceive a participatory management style at CareFree." A random sample of 200 CareFree employees is selected to test this hypothesis at the 0.05 level of significance.Ninety employees rate the management as participatory.The appropriate decision is ___.
A)do not reject the null hypothesis
B)reject the null hypothesis
C)reduce the sample size
D)increase the sample size
E)maintain status quo

Question

Quizplus · Accepted Answer

The null hypothesis is that the majority of employees do not perceive a participatory management style. The alternative hypothesis is that the majority of employees do perceive a participatory management style. The sample size is 200, and 90 employees rate the management as participatory. The sample proportion is 90/200 = 0.45. The standard error of the proportion is sqrt(0.45*0.55/200) = 0.05. The test statistic is (0.45 - 0.5)/0.05 = -1. The p-value is the probability of getting a test statistic as extreme as -1 or more extreme, assuming the null hypothesis is true. The p-value is 0.1587. Since the p-value is greater than the level of significance of 0.05, we do not reject the null hypothesis.

The Executives of CareFree Insurance, Inc