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).

1. Interpret the 95% confidence interval calculated by the student.

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2. The confidence interval (23.6, 27.3) can be referred to as a range of plausible values. For what is this the range of plausible values?

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3. When we say we have constructed a 95% confidence interval, what do we expect happens 95% of the time?

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4. If the student decreased the sample of marriage licenses issued in the last year in the county from 94 licenses to 40 marriage licenses while maintaining the same sample mean and sample standard deviation, what effect would the change in sample size have on the confidence interval? Explain.

1. Nothing, the interval will not change.
2. The interval will increase in width.
3. The interval will decrease in width.

Answer 1

1. We are 95% confident that the true population means age at which women marry in the country is lies between 23.6 and 27.3.

2. The confidence interval for the mean is the range of plausible values of the true population mean i.e. true population means is between 23,6 and 27.3 at 95% confidence level.

3. If we constructed many confidence interval using sample size of 94,95% of the confidence intervals will contain the population mean i.e. 95% of the time it will contain population mean.

4. The interval will increase in width.