In Exercises 5–16, use analysis of variance for the indicated test.

5. Lead and Verbal IQ Scores Example 1 used measured performance IQ scores for three different blood lead levels. If we use the same three categories of blood lead levels with measured verbal IQ scores, we get the accompanying Minitab display. (The data are listed in Data Set 7 “IQ and Lead” in Appendix B.) Using a 0.05 significance level, test the claim that the three categories of blood lead level have the same mean verbal IQ score. Does exposure to lead appear to have an effect on verbal IQ scores?

The output for the ANOVA test is stated from Minitab.

The significance level is 0.05.

To test the claim that three categories of blood lead levels have an equal level of mean verbal scores, the hypothesis is formulated as follows:

\(\begin{array}{l}{H_0}:{\mu _1} = {\mu _2} = {\mu _3}\\{H_a}:\;{\rm{at}}\;{\rm{least}}\;{\rm{one}}\;{\mu _i}\;{\rm{is}}\;{\rm{different}}{\rm{.}}\end{array}\)

Here,\({\mu _i}\)is the true mean verbal score for the ith blood lead level.

The decision rule for the test:

• The null hypothesis is rejected only when the p-value is lesser than the significance level.
• The null hypothesis fails to be rejected when the p-value is greater than or equal to the significance level.

From the output, the p-value is the value under the column header P, which is 0.677.

The p-value is larger than 0.05, which implies the null hypothesis fails to be rejected.

Thus, there is not sufficient evidence at the 0.05 significance level to warrant rejection of the claim that the verbal mean IQ scores for all blood lead levels are equal.

As per the conclusion, none of the mean IQ scores for the three categories of blood lead level differs from the others. Thus, it can be concluded that lead does not have any effect on verbal IQ scores as there is no statistically significant change in scores with changed blood lead levels.