Question

A national business magazine reports that the mean age of retirement for women executives is 62.9 . a women’s rights organization believes that this value does not accurately depict the current trend in retirement. to test this, the group polled a simple random sample of 81 recently retired women executives and found that they had a mean age of retirement of 61.6 . assuming the population standard deviation is 4.6 years, is there sufficient evidence to support the organization’s belief at the 0.05 level of significance? step 3 of 3 : draw a conclusion and interpret the decision.

Answer 1

There is sufficient evidence to support the organization's belief that the mean age of retirement for women executives is less than 62.9 years.

Step-by-step explanation:

To determine if there is sufficient evidence to support the women's rights organization's belief, we need to perform a hypothesis test. The null hypothesis, H0, is that the mean age of retirement for women executives is equal to 62.9 years. The alternative hypothesis, Ha, is that the mean age of retirement is less than 62.9 years, which supports the organization's belief.

We will use a one-sample t-test since we have a sample mean and the population standard deviation is known. The test statistic is calculated using the formula: t = (sample mean - population mean) / (population standard deviation / sqrt(sample size)). With a significance level of 0.05, we compare the test statistic to the critical value from the t-distribution table.

If the calculated test statistic is less than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to support the organization's belief. If the calculated test statistic is greater than or equal to the critical value, we fail to reject the null hypothesis.

Calculating the test statistic with the given values:

t = (61.6 - 62.9) / (4.6 / sqrt(81)) = -3.413

Using a t-distribution table, we find that the critical value at a significance level of 0.05 for a one-tailed test with 80 degrees of freedom is -1.663. Since the calculated test statistic of -3.413 is less than the critical value of -1.663, we reject the null hypothesis. Therefore, there is sufficient evidence to support the organization's belief that the mean age of retirement for women executives is less than 62.9 years.