Question

The data below represents the overall miles per gallon​ (MPG) of 2008 SUVs priced under​ $30,000.
Complete parts​ (a) and​ (b).
Start 2 By 1 Matrix 1st Row 1st Column 22 comma 18 comma 19 comma 21 comma 18 comma 19 comma 18 comma 17 comma 20 comma 20 comma 18 comma 2nd Row 1st Column 17 comma 20 comma 19 comma 20 comma 18 comma 17 comma 18 comma 16 comma 21 comma 18 comma 21 End Matrix. 22,18,19,21,18,19,18,17,20,20,18,17,20,19,20,18,17,18,16,21,18,21.

Construct a 99​% confidence interval estimate for the population mean miles per gallon of 2008 priced under​ $30,000 SUVs assuming a normal distribution. b. Interpret the interval constructed in​ (a).

Choose the correct answer below:

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

B.With 99​% ​confidence, the mean miles per gallon in the sample of 2008 SUVs is the population mean.

C. With 99 ​%​confidence, the mean miles per gallon in the population of 2008 SUVs is the sample mean.

D. With 99 ​% ​confidence, the mean miles per gallon in the sample of 2008 SUVs is somewhere in the interval.

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.