Question

In a recent study of 32 ninth-grade students, the mean number of hours per week that they played video games was 17.1. The standard deviation of the population was 2.8. Find the lower limit of the 95% confidence interval for the mean time for ninth-graders to play video games. Round your answer to the nearest tenth (one place after the decimal point).

Answer 1

First, we must find α

`\alpha=(1-0.95)/(2)=0.025`

Then, we must find Z in the Ztable,

That is z with a pvalue of

`1-0.025=0.975`

For this case,

`Z=1.96`

Then, we need to calculate the margin of error

`\begin{gathered} M=Z\cdot\frac{\sigma}{\sqrt[]{n}} \\ M=1.96\cdot\frac{2.8}{\sqrt[]{32}}=0.97 \end{gathered}`

Finally, the lower limit of the 95% confidence interval for the mean time for ninth-graders to play video games will be

`17.1-0.97=16.1`