Homework 15

Problems

General Instructions: For all confidence intervals you compute in these problems, draw a sketch of the confidence interval on the appropriate scale. For example, if you are told that a random sample of 25 individuals from a population whose height has standard deviation \(\sigma = 1 \text{ feet}\) has (sample) mean 6 feet, and are asked to compute a 95% confidence interval for the mean height in the population, then you should also sketch (you do not need the color-coding):

Section 8.1:

Note: For all confidence intervals in this section, you should assume that the population is Gaussian (normal) and the population standard deviation \(\sigma\) is known.

• 1
• 2
• 3 (be very careful in your interpretations)
• 4a-d
• 5ab

Section 8.3:

Note: For all confidence intervals in this section, you should assume that the population is Gaussian (normal) and the population standard deviation \(\sigma\) is unknown.

• 29. Use both R and Table A.5 and make sure your answers agree!
• 30. Use both R and Table A.5 and make sure your answers agree!
• 33. You may use R to generate a histogram, compute the sample mean and sample standard deviation, etc.
• 34. You may use R to generate a histogram, compute the sample mean and sample standard deviation, etc.
• 35a. Compute a two-sided confidence interval, rather than a lower confidence bound. We will discuss lower confidence bounds in the next class.