Question

The data below represents the overall miles per gallon​ (MPG) of 2008 SUVs priced under​ $30,000.

Answer 1

Answer:

99% Confidence interval: (17.9064,19.8136)

Step-by-step explanation:

We are given the following data set:

22,18,19,21,18,19,18,17,20,20,18,17,20,19,20,18,17,18,16,21,18,21

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$  

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.  

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{415}{22} = 18.86$

Sum of squares of differences = 52.59

$S.D = \sqrt{\frac{52.59}{21}} = 1.58$

99% Confidence interval:  

$\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}$  

Putting the values, we get,  

$t_{critical}\text{ at degree of freedom 21 and}~\alpha_{0.01} = \pm 2.831$  

$18.86 \pm 2.831(\frac{1.58}{\sqrt{22}} ) = 18.86 \pm 0.9536 = (17.9064,19.8136)$

Option A) With 99​% ​confidence, the mean miles per gallon in the population of 2008 SUVs is somewhere in the interval.