Question

In a third day of randomly selected subjects, the mean age of the 36 respondents is 40 years and the standard deviation of ages is 10 years. Use the sample results to construct a 95% confidence interval estimate of the mean age of the population from which the sample was selected. Repeat the previous problem assuming that the population standard deviation is known to be six years.

Answer 1

a. Given that:

- The mean age of the 36 respondents is 40 years.

- The standard deviation of ages is 10 years.

You need to construct a 95% confidence interval estimate of the mean age of the population from which the sample was selected.

Then, you need to use this formula:

`x\pm z\cdot(\sigma)/(√(n))`

Where "x" is the sample mean, "z" is the confidence level value, "n" is the sample size, and σ is the standard deviation.

In this case:

`\begin{gathered} x=40 \\ \sigma=10 \\ n=36 \end{gathered}`

Therefore, by substituting values into the formula:

`40\pm(10)/(√(36))`

You get these two values:

`40+(10)/(√(36))\approx41.67\text{ }`
`40-(10)/(√(36))\approx38.33`

b. If you assume that:

`\sigma=6`

You get the following values by substituting them into the formula:

`40+(6)/(√(36))=41`
`40-(6)/(√(36))=39`

Hence, the answers are:

a.

`(38.33,41.67)`

b.

`(39,41)`