Question

A sample of 14 randomly selected commuters in Chicago had an average commuting time of 39 minutes, with a standard deviation of 9.4 minutes. Find the lower limit of the 99% confidence interval of the true (population) mean. Round your answer to one place after the decimal point.

Answer 1

Given the confidence interval formular

Calculate the Margin of error

`\begin{gathered} \text{MOE}=\text{Critical value }* SE \\ \text{where} \\ SE=\frac{\sigma}{\sqrt[]{n}} \\ \sigma=9.4 \\ n=14 \end{gathered}`
`SE=\frac{9.4}{\sqrt[]{14}}=(9.4)/(3.7417)=2.5122`
`C.V\text{ for 99\% confidence significant level =}2.58`

Thus, the margin of error is

`\begin{gathered} \text{MOE}=CV* SE \\ =2.58*2.5122 \\ =6.48 \end{gathered}`

The confidence interval from the confidence interval formula will be

`\begin{gathered} CI=\bar{x}\pm MOE \\ =39\pm6.48 \\ =32.52<39<45.48 \end{gathered}`

Hence, the lower limit of the confidence interval will be 32.52