Question

Recently, a large academic medical center determined that 9 of 23 employees in a particular position were female​, whereas 43​% of the employees for this position in the general workforce were female. At the 0.05 level of​ significance, is there evidence that the proportion of females in this position at this medical center is different from what would be expected in the general​workforce?

What are the correct hypotheses to test to determine if the proportion is​ different?

A. H0​: π = 0.43​; H1​: π ≠ 0.43

B. H0​: π ≤ 0.43​; H1​: π > 0.43

C. H0​: π ≥ 0.43​; H1​: π < 0.43

D. H0​: π ≠ 0.43​; H1​: π = 0.43

Calculate the test statistic.

ZSTAT ___? (Type an integer or a decimal. Round to two decimal places as​ needed.)

What is the​ p-value?

The​ p-value is ___? ​(Type an integer or a decimal. Round to three decimal places as​ needed.)

State the conclusion of the test.

(Reject, Do not reject) the null hypothesis. There is (sufficient, insufficient) evidence to conclude that the proportion of females in this position at this medical center is different from the proportion in the general workforce.

Answer 1

The appropriate hypotheses for testing if the medical center's proportion of females in a particular position is different from the general workforce is H0: π = 0.43 and H1: π ≠ 0.43. The test statistic (ZSTAT) is calculated using the formula for a test of proportion and is compared to the significance level (alpha) to make a decision whether to reject or not reject the null hypothesis.

Step-by-step explanation:

In this scenario, we are testing whether the proportion of females at the medical center differs from the general workforce, where it is 43%. So, the correct null hypothesis H0 should state that there is no difference between the proportion at the medical center and the general workforce (H0: π = 0.43), whereas the correct alternative hypothesis H1 should suggest that there is a difference (H1: π ≠ 0.43). The hypotheses mentioned correspond to option A. To calculate the test statistic (ZSTAT), we use the formula for a test of proportion:

ZSTAT = (p' - π) / sqrt((π(1-π))/n)

Where p' is the sample proportion (9/23), π is the population proportion (0.43), and n is the sample size (23).

After calculating the ZSTAT, we would compare the resulting p-value to our alpha level, 0.05. If the p-value is less than 0.05, we reject the null hypothesis, indicating there is sufficient evidence to suggest that the proportion of females in this position at the medical center is significantly different from the general workforce.