Mr. Roby is trying to estimate the difference in the proportion of his male students who on average sleep fewer than 6 hours per night compared with his female students. He selects a random sample of 20 of his 75 male students and finds that 5 of them sleep fewer than 6 hours per night. He selects another random sample of 17 of his 100 female students and finds that 8 of them sleep fewer than 6 hours a night. Check the conditions for constructing a confidence interval for the difference in proportions. Random condition: 10% condition: Large Counts condition: | Are all the conditions for inference met?

Nearly one-half of Americans ages 25 to 29 are unmarried. How large a sample is necessary to estimate the true proportion of unmarried Americans in this age group within 2 percentage points with 95% confidence?

A random sample of 120 rhesus monkeys found that the number of rhesus monkeys that live in a captive breeding facility is 77. Construct a 90% confidence interval for the true proportion of rhesus monkeys that live in a captive breeding facility.

Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 7 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 3.6 hours with a standard deviation of 0.2 hours. For a random sample of 6 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 3.2 hours to paint each room with a standard deviation of 0.3 hours. At the 0.05 level, can Gary conclude that his meantime for painting a medium-sized room without using the tool was greater than his meantime when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using the…