Question

Jump to level 1Suppose the mean height in inches of all 9th grade students at one high school isestimated. The population standard deviation is 2 inches. The heights of 6randomly selected students are 65, 71, 73, 71, 71 and 64.= Ex: 12.34Margin of error at 90% confidence level = Ex: 1.2390% confidence interval = [Ex: 12.34 Ex: 12.34][smaller value, larger value]CheckNext2

Answer 1

First, let's calculate the sample mean. The mean is calculated by adding all values and dividing by the number of values:

`\begin{gathered} \bar{x}=(65+71+73+71+71+64)/(6)\\ \\ \bar{x}=(415)/(6)\\ \\ \bar{x}=69.17 \end{gathered}`

Now, for the margin of error, we can use the formula below:

`ME=z\cdot(\sigma)/(√(n))`

For a 90% interval, we use z = 1.645, so we have:

`\begin{gathered} ME=1.645\cdot(2)/(√(6))\\ \\ ME=1.343 \end{gathered}`
`\begin{gathered} ME=1.645\cdot(2)/(√(6))\\ \\ ME=1.34 \end{gathered}`

Then, the confidence interval is given by:

`\begin{gathered} (\bar{x}-ME,\bar{x}+ME)\\ \\ =\\ \\ (67.83,70.51) \end{gathered}`