In a population containing x^2 + 3 people, 8x + 3 people have blonde hair while 6x + 5 people have brown hair. What fraction of people in the population have at least one of these hair colors? ​

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.