Chapter 12.6, Problem 25PPS

To determine

To check : A hypothesis test to see that D is correct.

Explanation of Solution

Given information:

The following data represents D calculation for the last 30 tanks of gas of her car .

28.2	25.3	24.6	27.2	29.3	27.1	26.4	29.1	26.2	25.9
26.6	25.8	24.9	27.3	28.6	28.4	28.3	25.8	25.8	28.2
27.2	28.1	29.3	26.3	25.9	28.0	27.2	26.1	27.4	26.4

Hypotheses are,

  $\begin{array}{l}{H}_0:\mu =28\hfill \\ H_1:\mu <28\hfill \end{array}$

D collect the data for 30 tanks. And test the hypothesis using 95% confidence interval.

D collects the data for 30 tanks and notes the miles per gallon. Hence using excel functions "=average ()" for mean and "stdev()" for standard deviation the information for finding 95% confidence interval is,

  $\overline{x}=27.03,s=1.30,n=30$

The 95% confidence interval for mean is,

  $\begin{array}{l}\overline{x}\pm 1.96\cdot \frac{s}{\sqrt{n}}=27.03\pm 1.96\cdot \frac{1.30}{\sqrt{30}}\\ \begin{array}{l}=27.03\pm 0.47\hfill \\ =\left(26.56,27.50\right)\hfill \end{array}\end{array}$

Since confidence interval does not contain 28 so, one reject the null hypothesis. That is one can conclude that car averages less than 28 miles per gallon in city.