Question

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 __________.

Answer 1

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Answer 2

To determine the appropriate decision regarding the executives' hypothesis that a majority of employees perceive a participatory management style at CareFree Insurance, Inc., we need to conduct a hypothesis test.

Let's state the null and alternative hypotheses: Null hypothesis (H0): The proportion of employees perceiving a participatory management style is equal to 0.50 (no majority perception). Alternative hypothesis (H1): The proportion of employees perceiving a participatory management style is greater than 0.50 (majority perception).

We will use a one-sample proportion hypothesis test. The test statistic for this hypothesis test is the z-score, which can be calculated as follows:

z = (p - P) / sqrt(P(1 - P) / n)

Where: p is the sample proportion (90/200 = 0.45) P is the hypothesized population proportion (0.50) n is the sample size (200)

Calculating the z-score: z = (0.45 - 0.50) / sqrt(0.50 * (1 - 0.50) / 200) z ≈ -1.7678

Next, we need to find the critical value for a one-tailed test at the 0.05 level of significance. Since we are testing whether the proportion is greater than 0.50, we need to look up the critical value for the upper tail.

Looking up the z-score in the standard normal distribution table, we find that the critical value for a one-tailed test at the 0.05 level of significance is approximately 1.645.

Since the calculated z-score (-1.7678) is less than the critical value (1.645), we fail to reject the null hypothesis. This means that there is not enough evidence to support the claim that a majority of employees perceive a participatory management style at CareFree Insurance, Inc.

Therefore, the appropriate decision is to fail to reject the null hypothesis.