The Centers for Disease Control and Prevention (CDC) define a healthy sleep duration to be at least seven hours per day. The CDC reports that the percentage of people who report a healthy sleep duration varies by marital status. The CDC also reports that in 2018, 67% of those who are married report a healthy sleep duration; 62% of those who have never been married report a healthy sleep duration; and 56% of those who are divorced, widowed, or separated report a healthy sleep duration. The file SleepHabits contains sample data on the sleeping habits of people who have never been married that are consistent with the CDC’s findings. Use these data to answer the following questions. 

a. Develop a point estimate and a 95% confidence interval for the proportion of those who have never been married who report a healthy sleep duration. 

b. Develop a point estimate and a 95% confidence interval for the mean number of hours of sleep for those who have never been married. 

c. For those who have never been married, estimate the number of hours of sleep per day for those who report a healthy sleep duration.