8.6 A large laboratory has four types of devices used to determine the pH of soil samples. The laboratory wants to determine whether there are differences in the average readings given by these devices. The lab uses 24 soil samples having known pH in the study and randomly assigns six of the samples to each device. The soil samples are tested, and the response recorded for each sample is the difference between the pH reading of the device and the known pH of the soil. These values, along with summary statistics, are given in the following table. Sample Device 1 2 3 4 5 6 A -.307 -.294 .079 .019 -.136 -.324 B -.176 .125 -.013 .082 .091 .459 C .137 -.063 .240 -.050 .318 .154 D -.042 .690 .201 .166 .219 .407 a. Based on your intuition, is there evidence to indicate any difference among the mean differences in pH readings for the four devices? b. Run an analysis of variance to confirm or reject your conclusion in part (a). Use a 5 .05. c. Compute the p-value of the F test in part (b). d. What conditions must be satisfied for your analysis in parts (b) and (c) to be valid? e. Suppose the 24 soil samples have widely different pH values. What problems may occur by simply randomly assigning the soil samples to the different devices?
8.6
A large laboratory has four types of devices used to determine the pH of soil samples. The laboratory wants to determine whether there are differences in the average readings given by these devices. The lab uses 24 soil samples having known pH in the study and randomly assigns six of the samples to each device. The soil samples are tested, and the response recorded for each sample is the difference between the pH reading of the device and the known pH of the soil. These values, along with summary statistics, are given in the following table.
Sample
| Device | 1 | 2 | 3 | 4 | 5 | 6 |
| A | -.307 | -.294 | .079 | .019 | -.136 | -.324 |
| B | -.176 | .125 | -.013 | .082 | .091 | .459 |
| C | .137 | -.063 | .240 | -.050 | .318 | .154 |
| D | -.042 | .690 | .201 | .166 | .219 | .407 |
a. Based on your intuition, is there evidence to indicate any difference among the mean differences in pH readings for the four devices?
b. Run an analysis of variance to confirm or reject your conclusion in part (a). Use a 5 .05.
c. Compute the p-value of the F test in part (b).
d. What conditions must be satisfied for your analysis in parts (b) and (c) to be valid?
e. Suppose the 24 soil samples have widely different pH values. What problems may occur by simply randomly assigning the soil samples to the different devices?
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