Chapter 14.5, Problem 31E

a.

To determine

Find the standard error of the mean.

Answer to Problem 31E

  $0.57$

Explanation of Solution

Given information:

Given: Ten families were interviewed on the basis of their television viewing habits. The average number of hours that these families had their televisions on per day was $4.1hours$ with the standard deviation $1.8hours$ .

Calculation:

Here, we have to find the standard error of the mean:

  $\begin{array}{l}{\sigma }_{\overline{X}}=\frac{Standarddeviation}{\sqrt{N}}\\ {\sigma }_{\overline{X}}=\frac{1.8}{\sqrt{10}}=0.57\end{array}$

Hence, the standard error of the mean is $0.57$ .

b.

To determine

Find the interval about the sample mean having $5\%$ confidence level.

Answer to Problem 31E

  $\left[2.98,5.22\right]$

Explanation of Solution

Given information:

Given: Ten families were interviewed on the basis of their television viewing habits. The average number of hours that these families had their televisions on per day was $4.1hours$ with the standard deviation $1.8hours$ .

Calculation:

Here, we have to find the interval:

  $\begin{array}{l}5\%confidencelevelmeansP=95\%\\ P=95\%correspondstot=1.96\\ \left[\overline{X}-t{\sigma }_X,\overline{X}+t{\sigma }_X\right]\\ \left[2.98,5.22\right]\end{array}$

Hence, the interval is $\left[2.98,5.22\right]$ .

c.

To determine

Draw the inferences of about the television habits from the data.

Answer to Problem 31E

  $none$

Explanation of Solution

Given information:

Given: Ten families were interviewed on the basis of their television viewing habits. The average number of hours that these families had their televisions on per day was $4.1hours$ with the standard deviation $1.8hours$ .

Calculation:

Here, no sample is too small to generalize to the population of the city.

Hence, the required answer is $none$ .