Chapter 11 Minitab Instructions
Testing p1-p2
A. (Replicating Example 11.3) From the menu choose Stat > Basic Statistics > 2 Proportions.
Choose Summarized data. For First, enter 5400 for Events and 6000 for Trials. For
Second, enter 8600 for Events and 10000 for Trials.
B. Choose Options. Enter 0 for Test difference. Select ‘greater than’ for Alternative. Select
Use pooled estimate of p for test. Click OK.
C. Minitab reports the following results. The value of the test statistic of 7.41 (in boldface)
matches the one obtained in Example 11.3.
Test and CI for Two Proportions
Sample
1
2
X
5400
8600
N
6000
10000
Sample p
0.900000
0.860000
Difference = p (1) - p (2)
Estimate for difference: 0.04
95% lower bound for difference: 0.0314468
Test for difference = 0 (vs > 0): Z = 7.41
Fisher's exact test: P-Value = 0.000
1
P-Value = 0.000
Goodness-of-Fit Test
A. (Replicating Example 11.5) Input the data from Table 11.5 into a Minitab spreadsheet.
Remember to combine the data for Firms 4 and 5.
B. From the menu choose Stat > Tables > Chi-Square Goodness-of-Fit Test (One Variable).
Choose Observed counts and then select Number of Recent Customers. For Test, select
Specific proportions and then select Market Share.
C. Choose Results. Select Display test results. Click OK.
D. Minitab reports the following results. The value of the test statistic (in boldface) matches the
one obtained in Example 11.5. In addition, Minitab reports the exact p-value of 0.017.
Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: Number of Rece
Category
1
2
3
4
N
200
DF
3
Observed
70
60
54
16
Chi-Sq
10.25
Historical
Counts
0.40
0.32
0.24
0.04
Test
Proportion
0.40
0.32
0.24
0.04
Expected
80
64
48
8
P-Value
0.017
2
Contribution
to Chi-Sq
1.25
0.25
0.75
8.00
Chi-Square Test of Independence
A. (Replicating Example 11.6) Copy the data from Table 11.9 into a Minitab spreadsheet. Do
not include the row totals or the column totals.
B. From the menu choose Stat > Tables > Chi-Square Test (Two Way Table in Worksheet).
In the Chi-Square Test dialog box, select Economy Car and Noneconomy Car for Columns
containing the table. Click OK.
C. Minitab reports the following results. The expected frequency for each cell is shown below
the observed frequency. In addition, Minitab shows each cell’s chi-square contributions
below the expected frequency. The value of the test statistic (in boldface) almost matches the
one obtained in Example 11.6 – the values differ due to rounding. In addition, Minitab
reports the exact p-value of 0.462.
Chi-Square Test: Economy Car, Noneconomy Car
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
Economy
Car
50
46.75
0.226
Noneconomy
Car
60
63.25
0.167
2
120
123.25
0.086
170
166.75
0.063
290
Total
170
230
400
1
Total
110
3
Chi-Sq = 0.542, DF = 1, P-Value = 0.462
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