A study of 203 police officers in an eastern state found that their mean salary was $75,500 with a sample standard deviation of $3,000. The same study of 245 police officers in a northern state found that their mean salary was $74,500 with a sample standard deviation of $4,000. Let group 1 be the eastern state police officers and group 2 be the northern state police officers.

1. Find the lower bound of a 95% confidence interval for the mean salary difference of police officers between an eastern state and a northern state.

2. Find the upper bound of a 95% confidence interval for the mean salary difference of police officers between an eastern state and a northern state.

3. Find the lower bound of a 95% confidence interval for the mean salary difference of police officers between an eastern state and a northern state. Let us assume that the standard deviations for both groups are the same.

4. Find the upper bound of a 95% confidence interval for the mean salary difference of police officers between an eastern state and a northern state. Let us assume that the standard deviations for both groups are the same.

Suppose the salaries of 61 police officers among 203 police officers in an eastern state and 81 police officers among 245 police officers in a northern state were over $100,000.

5. Find the lower bound of a 95% confidence interval for the difference in proportions of over $100,000 salaries between the two groups.

6. Find the upper bound of a 95% confidence interval for the difference in proportions of over $100,000 salaries between the two groups.