A company is criticized because only 14 of 41 executives at a local branch are women. The company explains that although this proportion is lower than it might wish, it's not a surprising value given that only 43% of all its employees are women. The company has more than 500 executives worldwide. Test an appropriate hypothesis and state the conclusion. I just don't know how to begin
To test an appropriate hypothesis in this case, we can use a hypothesis test for proportions. Specifically, we can compare the proportion of women executives at the local branch to the proportion of women among all employees in the company.
Here's how we can proceed with the hypothesis test:
1. State the null hypothesis (H0) and the alternative hypothesis (H1):
- H0 (Null Hypothesis): The proportion of women executives at the local branch is equal to the proportion of women among all employees in the company.
- H1 (Alternative Hypothesis): The proportion of women executives at the local branch is significantly different from the proportion of women among all employees in the company.
2. Select a significance level (α) to determine the threshold for rejecting the null hypothesis. Common choices for α are 0.05 or 0.01.
3. Collect the necessary data:
- From the given information, we know that there are 41 executives at the local branch, with only 14 of them being women.
- We are also told that only 43% of all company employees are women. We can use this proportion to compare with the proportion at the local branch.
4. Calculate the test statistic:
- In this case, we will use the z-test for comparing proportions.
- The formula to calculate the z-test statistic for comparing two proportions is:
z = (p1 - p2) / sqrt((p * (1 - p) * (1/n1 + 1/n2)))
where:
- p1: Proportion of women at the local branch
- p2: Proportion of women in the company
- n1: Sample size at the local branch (41 executives)
- n2: Sample size of all company employees (more than 500 executives)
- p: Pooled proportion, calculated as (x1 + x2) / (n1 + n2)
where x1 is the number of women at the local branch, and x2 is the number of women in the company.
5. Determine the critical region and calculate the p-value:
- Given the null hypothesis, we can calculate the critical value or find the p-value based on the test statistic.
- The critical region consists of extreme values that would lead to rejecting the null hypothesis.
- If the p-value is smaller than the significance level (α), we reject the null hypothesis.
6. State the conclusion:
- If the p-value is greater than the significance level (α), we fail to reject the null hypothesis. This suggests that the difference in the proportion of women executives at the local branch and the proportion of women in the company could be due to random chance alone.
- If the p-value is smaller than the significance level (α), we reject the null hypothesis. This implies that the difference in proportions is statistically significant and likely not due to random chance alone.
Note: It's important to perform the calculations using the specific data provided in order to reach a conclusion based on the hypothesis test.