Question

Question 6:

From a random sample of 80 women, 48 say they have been sexually harassed. From another random sample of 65 men, 13 say they have been sexually harassed. Construct a 95% confidence interval for the difference between the proportions of women and men who say they have been sexually harassed.

If the problem is a confidence interval:

• Show whether the criteria for approximate normality are met. (1 point)

• Summarize the sample statistics. (1 point)

• Give the formula for the margin of error or test statistic. (1 point)

• Give the formula for the confidence interval. (1 point)

• Based on the technology results provided, write the 95% confidence interval. (3 points)

• Interpret the results in the context of the problem (3 points)

If the problem is a hypothesis test:

• Give the null and alternative hypotheses; (2 points)

• Is this a one‐tailed or two‐tailed test? Think about the null hypothesis. How do you know
  that this is a one or two‐tailed test? (1 point)

• Show whether the criteria for approximate normality are met. (1 point)

• Summarize the sample statistics (1 point)

• Give the formula for the test statistic; (1 point)

• Using the technology results provided, point out the value for the test statistics, degree of
  freedom, and the p-value. (1 point)

• Using the p-value and the significance level, make a decision on the null hypothesis. (1
  point)

• What decision can you make about the alternative hypothesis? (1 point)

• Write your conclusion in the context of the problem. (1 point)

Answer 1

If the problem is a confidence interval:
The criteria for approximate normality is met because the sample sizes of both the two groups are greater than 30.
The sample statistics: .
Interpret the results in the context of the problem -> We are 95% confident that the difference between the proportions of women and men who say they have been sexually harassed will lie between 0.2552 and 0.5448. The interval contains only positive values, indicating that the proportion of women being sexually harassed is much higher than the proportion of men.


If the problem is a hypothesis test:
The criteria for approximate normality is met because the sample sizes of both the two groups are greater than 30.
The sample statistics: , = pooled proportion = 0.421.
Since the p-value is less than the significance level of 0.05, our decision is that we reject the null hypothesis, H0. We accept the alternative hypothesis.
We conclude that there is enough sample evidence to suggest that there exists a significant difference between the proportions of women and men who say they have been sexually harassed.