EXAMPLE 6 intervals for using technology
highwaympg 16
Motor Vehicle Fuel Efficiency
Another of the variables in our case study is Highway MPG, which is the number of miles a vehicle can travel on a highway on one gallon of gas. We know the population standard deviation . The sample of 16 vehicles, shown here, has a sample mean highway gas mileage of .
| Vehicle | Highway MPG | Vehicle | Highway MPG |
|---|---|---|---|
| Honda CR-V | 30 | Subaru Impreza | 25 |
| Nissan Pathfinder | 26 | Ford Mustang | 26 |
| Acura MDX | 28 | Cadillac ATS | 31 |
| Porsche Cayenne | 29 | Chevrolet Camaro | 24 |
| Mercedes-Benz GLK 250 | 33 | Ford Taurus | 29 |
| Chevrolet Chevy SS | 21 | Ford Expedition | 20 |
| Dodge Charger | 27 | Lincoln MKT | 25 |
| Jeep Compass | 23 | BMW X1 | 34 |
- Determine whether the interval for may be applied.
- Use the TI-83/84, Minitab, and JMP to construct a 95% confidence interval for the population mean Highway MPG.
Solution
- The sample size is not large , so we need to check if the data follow a normal distribution. The normal probability plot of the data in Figure 4 supports the assumption of normality. Further, the population standard deviation is known. We may thus apply the interval for .
Figure 8.4: FIGURE 4 Normal probability plot of the Highway MPG data. We shall use the instructions provided in the Step-by-Step Technology Guide at the end of this section (page 441). The results for the TI-83/84 in Figure 5 show that the 95% confidence interval for the population mean Highway MPG is
Figure 5 also shows the sample mean , the sample standard deviation , and the sample size .
Figure 8.5: FIGURE 5 TI-83/84 results.
The Minitab results are provided in Figure 6. The “assumed standard deviation” is indicated to be . Then the sample size , the sample mean , and the sample standard deviation are displayed. “SE Mean” refers to the standard error of the mean, but we don't need it here. Finally, the 95% confidence interval is given as (lower bound = 23.84, upper bound = 30.04).
437
The JMP results are shown in Figure 7. The sample mean is shown in the first column, with the sample standard deviation below it. The 95% confidence interval is given in the row labeled Mean, with lower bound = 23.84 (rounded) and upper bound = 30.04 (rounded).
