Supply & Demand
Examples 6.3, 6.4, and 6.5 (page 338) – Large Sample Hypothesis Test of a
Mean
Example 6.3
A manufacturer of cereal wants to test the performance of one of its filling machines. The machine is designed to discharge a mean amount of 12 ounces per box, and the manufacturer wants to detect any departure from this setting. This quality study calls for randomly sampling 100 boxes from today’s production run and determining whether the mean fill for the run is 12 ounces per box. Set up a test of hypothesis for this study, using an alpha level of .01
Since the manufacturer is interested in any departure (more than 12 or less than 12) from a mean of 12 ounces the appropriate alternate hypothesis is µ ≠ 12.
Therefore H0: µ = 12 and H1: µ ≠ 12
Example 6.4
Example 6.4 asks you to conduct the test from Example 6.3. This tutorial will demonstrate how to use Minitab to conduct the test.
Figure 6.5 in the text visually represents the structure of the test. Any Z value larger than 2.575 or smaller than
–2.575 will result in the acceptance of the alternate hypothesis (i.e., that the mean fill weight of the machine is not equal to 12.
Example 6.5
Find the observed significance level for the test of the mean filling weights in Examples 6.3 and 6.4. This tutorial will demonstrate how to use Minitab to find the significance level for the test.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Click on Stat.
Click on Basic Statistics.
Click on Display Descriptive Statistics We need to get a value for the standard deviation in order to conduct the test.
Double-click FILL.
Click the OK button (note the value for the sample standard deviation, .512 for this example).
Click on Stat.
Click on Basic Statistics.
We will use a large sample test of a population mean because our sample size is >30. Therefore, click on 1Sample Z.
Because the data is in the first column of the worksheet, click in the Samples in columns text box.
Double-click the column
Mean
Example 6.3
A manufacturer of cereal wants to test the performance of one of its filling machines. The machine is designed to discharge a mean amount of 12 ounces per box, and the manufacturer wants to detect any departure from this setting. This quality study calls for randomly sampling 100 boxes from today’s production run and determining whether the mean fill for the run is 12 ounces per box. Set up a test of hypothesis for this study, using an alpha level of .01
Since the manufacturer is interested in any departure (more than 12 or less than 12) from a mean of 12 ounces the appropriate alternate hypothesis is µ ≠ 12.
Therefore H0: µ = 12 and H1: µ ≠ 12
Example 6.4
Example 6.4 asks you to conduct the test from Example 6.3. This tutorial will demonstrate how to use Minitab to conduct the test.
Figure 6.5 in the text visually represents the structure of the test. Any Z value larger than 2.575 or smaller than
–2.575 will result in the acceptance of the alternate hypothesis (i.e., that the mean fill weight of the machine is not equal to 12.
Example 6.5
Find the observed significance level for the test of the mean filling weights in Examples 6.3 and 6.4. This tutorial will demonstrate how to use Minitab to find the significance level for the test.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Click on Stat.
Click on Basic Statistics.
Click on Display Descriptive Statistics We need to get a value for the standard deviation in order to conduct the test.
Double-click FILL.
Click the OK button (note the value for the sample standard deviation, .512 for this example).
Click on Stat.
Click on Basic Statistics.
We will use a large sample test of a population mean because our sample size is >30. Therefore, click on 1Sample Z.
Because the data is in the first column of the worksheet, click in the Samples in columns text box.
Double-click the column