# Two hypothesis testing questions

1. Suppose that the mean of the annual return for common stocks from 2000 to 2012 was 14.37%, and the standard deviation of the annual return was 35.14%. Suppose also that during the same 12-year time span, the mean of the annual return for long-term government bonds was 0.6%, and the standard deviation was 2.1%. The distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric in this scenario. 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 16.32%.

b. Find the probability that the return for common stocks will be greater than 5.89%.

c. Find the probability that the return for common stocks will be less than 14.37%.

2. The management of a computer software company is considering relocating the corporate office (A) to a new location out of state, office (B). The management is concerned that the commute times of the employees to the new office (B) might be too long. The company decides to survey a sample of employees at other companies in the same office (A) to see how long these employees are commuting to the office. A sample of 23 employees indicated that the employees are commuting X (bar) = 33 minutes and s = 1 minute, 45 seconds.

1. a. Using the 0.01 level of significance, is there evidence that the population mean is above 32 minutes?

2. b. What is your answer in (a) if X (bar) = 37 minutes and s = 27 minutes?

3. c. Look at your answers for a and b above and discuss what you can learn from the results about the effect of a large standard deviation.

#### Solution Preview

1. Suppose that the mean of the annual return for common stocks from 2000 to 2012 was 14.37%, and the standard deviation of the annual return was 35.14%. Suppose also that during the same 12-year time span, the mean of the annual return for long-term government bonds was 0.6%, and the standard deviation was 2.1%. The distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric in this scenario. 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 16.32%.

Since distribution of annual returns for common stocks is bell-shaped and approximately symmetric in this scenario, it is normally ...

#### Solution Summary

The solution gived detailed steps on hypothesis testing. All formula and calculations are shown and explained.