In a statistics course project, students are interested in the proportions of 1st year and 4th year students at UW-Madison students who have remained in Madison (in an apartment or in a residence hall) and the proportion that have returned home after courses moved to an online format after spring break. The following data shows the results of a survey. Analyze the data as if the respondents to the survey represent random samples from the populations of 1st and 4th year UW-Madison students. stayed returned 1st year 19 68 4th year 36 17 15 Find a 95% confidence interval for the difference in population proportions who returned home after spring break using a formula. Interpret the confidence interval in context.

The 95% confidence interval for the difference in population proportions who returned home after spring break is (0.31, 0.61).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference between two population proportions is:

The information provided is:

                Stayed    Returned

1st year          19           68

4th year        36            17

Compute the sample proportion of 1st year students who returned home as follows:

Compute the sample proportion of 4th year students who returned home as follows:

The critical value of z for 95% confidence level is:

Compute the 95% confidence interval for the difference between two proportions as follows:

Thus, the 95% confidence interval for the difference in population proportions who returned home after spring break is (0.31, 0.61).

The 95% confidence interval for difference between two population proportions, (0.31, 0.61) implies that there is a 0.95 probability that the true difference between the proportions is included in the interval.

e

step-by-step explanation:

an equation by definition has to have two or more variables (x and 2 in this case)