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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.

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