A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval for the mean was calculated to be (2181260 comma 5836180 ). Explain what the phrase "90% confident" means.

The confidence interval for the mean is given by the following formula:

  (1)

For this case the confidence is 90% and the interva calculated for the true mean of total compensation of CEOs in the service Industry is given by:

So we can conclude that we have 90% of confidence that the true mean for the total compensation of CEOs in the service industry is between 2181260 and 5836180

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

s represent the sample standard deviation

n=18 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

  (1)

For this case the confidence is 90% and the interva calculated for the true mean of total compensation of CEOs in the service Industry is given by:

So we can conclude that we have 90% of confidence that the true mean for the total compensation of CEOs in the service industry is between 2181260 and 5836180