Question

1. A laboratory has four types of devices used to determine the pH of soil samples. The scientists who work there want to know whether there are differences in the average readings given by these devices. There were 24 soil samples with known pH levels. These soil samples were randomly assigned to each of the four devices (six samples each). The pH readings for each sample and device were recorded and an ANOVA was run on the data.

Source                                     DF        Sum of Squares                       Mean Square F Value      Pr>F     

Model                                         0.584                                                              4.85               0.0108

Error                                           0.803

Corrected Total                          1.387

a. Fill in the missing degrees of freedom and mean squares in the ANOVA table.

b. Identify the design in this experiment.

c. Write out the effects form of the linear model for this experiment and label the effects.

d. Perform an appropriate hypothesis test. Clearly state the null and alternative hypotheses and the conclusion in terms of the original experiment.

Answer 1

One-way ANOVA: A, B, C, D Source DF Factor 3 0.5837 0.1946 4.85 0.011 Error 20 0.8029 0.0401 Total 23 1.3866 MS S 0.2004 R-Sq 42.10% R-Sq ( adj ) 33.41% - From the above output, the test statistic F-4.85 Since the value of F does not exceed the tabulated value 3.10 at a -.05, df-3, df-20. So there is sufficient evidence to reject the null hypothesis.