# Solution assignment 01 of Estimation

1. Annual income presidents
The data for this assignment are listed in the Excel file Annual income presidents.
A survey of 80 randomly selected companies asked them to report the annual income of their presidents. Assume that incomes are normally distributed with a standard deviation of 30,000 dollar.
a. Determine the 90% confidence interval estimate of the annual income of all company presidents. Interpret the statistical results.
b. What would happen to the interval width if we take the 95% confidence interval?
c. What would happen to the interval width if 250 randomly selected companies had been asked. Explain your answer.

Solution.
a. The 90% confidence interval estimate is .  The sample mean is dollar (computed from the data in the data file), the population standard deviation was given (30,000 dollar), the sample size is  and . This results in the interval . We estimate that the mean annual income of all company presidents lies in this interval; this type of estimate is correct 90% of the time.
b. If the 95% confidence interval estimate was taken then only  changes which becomes larger: . The 95% confidence interval will be wider.
c. Now  will be larger and thus the interval will be narrower.