Please show the work to get the following answers for these questions

5. The following random sample was selected : 4, 6, 3, 5, 9, 3. Find the 95% confidence interval for the mean of the population.

95% confidence interval is between2.6070and7.3930

6. In a sample of 35 high school seniors, 14 of them are attending college in the fall. Find the 95% confidence interval for the true proportion of high school seniors that will attend college in the fall from the population.

16.33%-16.53%

7. In a sample of 200 people, 76 people would rather work out at home than in a gym. Find the 99% confidence interval for the true proportion of people who would rather work out at home than in a gym for the entire population.

71.2%-71.4%