Question

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.

Answer 1

Answer:

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$   (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:

$2181260 \leq \mu \leq 5836180$

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".

$\bar X$ represent the sample mean for the sample  

$\mu$ 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:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$   (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:

$2181260 \leq \mu \leq 5836180$

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