EXAMPLE 32 test for using the -value method and technology

The table contains the calories in ten entrée food items, courtesy of Food-A-Pedia. Test whether the population standard deviation is larger than 100 calories, using level of significance .

entreecalories

Entrée item Calories Entrée item Calories
Grilled steak 387 Ground beef (95% lean,
medium patty)		 167
Fried steak 440 Grilled pork chop (large) 314
Breaded fried steak 600 Fried pork chop (large) 326
Ground beef (75% lean, medium
patty)		 234 Meat pizza, thin crust, large 325
1 large BBQ short rib with sauce 148 Fried catfish (breaded or
battered)		 276

Solution

The normal probability plot in Figure 45 indicates acceptable normality, allowing us to proceed with the hypothesis test.

image
Figure 9.56: FIGURE 45 Normal probability plot of calories.

  • Step 1 State the hypotheses and the rejection rule.

    The phrase “larger than” indicates that we have a right-tailed test. The question “Larger than what?” tells us that , giving us

    We reject if the .

  • Step 2 Find .

    We use the Step-by-Step Technology Guide on page 562. The Minitab descriptive statistics in Figure 46 tell us that the sample variance is calories squared.

    image
    Figure 9.57: FIGURE 46 Calories descriptive statistics.

    Thus,

  • Step 3 Find the -value.

    For our right-tailed test, Table 14 tells us that

    That is, the -value is the area to the right of , as shown in Figure 47. To find the -value, we use the instructions provided in the Step-by-Step Technology Guide provided at the end of this section. The TI-83/84 results shown in Figure 48 tell us that .

    image
    Figure 9.58: FIGURE 47 -Value for test
    image
    Figure 9.59: FIGURE 48 TI-83/84 results.

  • Step 4 State the conclusion and the interpretation.

    Because is not , we do not reject . There is insufficient evidence that the population standard deviation is greater than 100 calories.

NOW YOU CAN DO

Exercises 13–18.