Lead and Full 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 the fullIQ scores, we get the accompanying Excel 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 full IQ score. Does it appear that exposure to lead has an effect on full IQ scores?

ANOVA output is stated from Excel.

The significance level is 0.05.

The test claims to establish whether the mean full scores of IQ vary across three categories of blood lead levels.

The hypotheses are stated below.

\[\begin{array}{l}{H_0}:{\mu _1} = {\mu _2} = {\mu _3}\\{H_a}:\;at\;least\;one\;{\mu _i}\;is\;different\end{array}\]

Here, \({\mu _i}\)is the actual mean full IQ scores under the three lead blood levels.

From the Excel output, the p-value is obtained from the column with the header p-value.

The p-value is 0.104395.

The decision rule:

When thep-value is greater than 0.05, fail to reject the null hypothesis.

When the p-value is less than 0.05, reject the null hypothesis.

Since the p-value is greater than 0.05, the null hypothesis fails to be rejected at the 0.05 significance level. Thus, there is not sufficient evidence to warrant rejection of the claim that the mean full IQ scores for all lead levels are equal at the 0.05 significance level.

As none of the mean full IQ scores under the three different categories of blood lead level differs as per the ANOVA result, it can be concluded that changes in the lead level do not affect the scores.

The statistical results are conclusive of the fact that as the lead levels change, the mean full IQ score does not show any significant change.