Question

A student wants to study the ages of women who apply for marriage licenses in his county. He selects a random sample of 94 marriage licenses issued in the last year in the county and makes a 95% confidence interval for the mean age at which women marry. The 95% confidence interval is (23.6, 27.3).Interpret the 95% confidence interval calculated by the student.

Answer 1

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

`\bar X \pm t_(\alpha/2)(s)/(√(n))` (1)

For this case the confidence interval obtained is: (23.6 ; 27.3)

And the best interpretation would be:

We have 95% of confidence that the true mean os ages of women who apply for marriage licenses in his county is between 23.6 and 27.3

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=94 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)(s)/(√(n))` (1)

For this case the confidence interval obtained is: (23.6 ; 27.3)

And the best interpretation would be:

We have 95% of confidence that the true mean os ages of women who apply for marriage licenses in his county is between 23.6 and 27.3