# Confidence interval

Probability

1. According to Investment Digest ("Diversification and the Risk/Reward Relationship", Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 14.4%, and the standard deviation of the annual return was 20.5%. During the same 67-year time span, the mean of the annual return for long-term government bonds was 5.5%, and the standard deviation was 7.0%. The article claims that the distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric. Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously.

a. Find the probability that the return for common stocks will be greater than 0%.

b. Find the probability that the return for common stocks will be less than 20%.

Hint: There are many ways to attack this problem in the HW. If you would like the normal distribution table so you can draw the pictures (my preferred way of learning) then I suggest you bookmark this site:

Confidence Interval Estimation

2. Compute a 95% confidence interval for the population mean, based on the sample 1, 2, 3, 4, 5, 6, and 35. Change the number from 35 to 15 and recalculate the confidence interval. Using the results, describe the effect of an outlier or extreme value on the confidence interval.

Hypothesis Testing

3. The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 20 students enrolled in the university indicates that X (bar) = $315.4 and s = $43.20.

a. a. Using the 0.10 level of significance, is there evidence that the population mean is above $300?

b. b. What is your answer in (a) if s = $75 and the 0.05 level of significance is used?

c. c. What is your answer in (a) if X (bar) = $305.11 and s = $43.20?

d. d. Based on the information in part (a), what decision should the director make about the books used for the courses if the goal is to keep the cost below $300?

#### Solution Summary

Step by step method for construction of confidence interval is discussed here. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems.