. A certain researcher thinks that the proportion of women who say that female bosses are harshly critical is greater than the proportion of men.

In a random sample of 200 women, 27% said that female bosses are harshly critical.

In a random sample of 220 men, 25% said that female bosses are harshly critical.

To determine whether there is evidence to support the researcher's claim, we can conduct a hypothesis test. The null hypothesis (H₀) assumes that there is no difference between the proportions of women and men who say that female bosses are harshly critical, while the alternative hypothesis (H₁) assumes that the proportion of women is greater.

Let's walk through the steps to conduct this hypothesis test:

1. Define the null and alternative hypotheses:
H₀: p₁ = p₂ (proportion of women = proportion of men)
H₁: p₁ > p₂ (proportion of women > proportion of men)

2. Calculate the sample proportions:
For women: 27% of 200 = 0.27 * 200 = 54
For men: 25% of 220 = 0.25 * 220 = 55

3. Calculate the standard errors:
For women: sqrt((0.27 * 0.73) / 200) ≈ 0.0289
For men: sqrt((0.25 * 0.75) / 220) ≈ 0.0273

4. Calculate the test statistic (z-score):
z = (p₁ - p₂) / sqrt((p₁ * (1 - p₁) / n₁) + (p₂ * (1 - p₂) / n₂))
= (0.27 - 0.25) / sqrt((0.27 * 0.73 / 200) + (0.25 * 0.75 / 220))
≈ 1.1

5. Determine the critical value:
Depending on the desired level of significance (α), we can look up the critical value from the z-table. Let's assume α = 0.05, which corresponds to a one-tailed test. The critical value for a 0.05 significance level is approximately 1.645.

6. Compare the test statistic and critical value:
Since the test statistic (1.1) is less than the critical value (1.645), we fail to reject the null hypothesis.

7. Draw a conclusion:
Based on the data, there is insufficient evidence to suggest that the proportion of women who say that female bosses are harshly critical is greater than the proportion of men.

Note: It's important to emphasize that this conclusion is based solely on the samples provided. It may not necessarily represent the true population proportions, and further research may be required.