Researchers are concerned that exposure to lead pollution may reduce brain development in children.They collect a sample of 121 children who live within a 4 mile radius of a lead smelter and measure their IQ as well as the amount of lead found in their bloodstream.Children are then broken into three groups: a group that has a low amount of lead in their blood, a group that has a medium amount of lead in their blood, and a group that has a high amount of lead in their blood.Statistics for these samples are listed in the table below:

Data

Statistics

Low Lead Group

Medium Lead Group

High Lead Group

Mean IQ

102.7

94.1

94.2

Standard Deviation

16.8

15.5

11.4

Sample Size

78

22

21

In addition to these statistics, researchers also constructed box plots to compare the distributions:

Graphs

Using statistical software, they obtain the following ANOVA output:

ANOVA Output

Df

Sum of Squares

Mean Square

F

Pr(>F)

Lead Level

2

2022.730

1011.365

4.071

0.01951

Residuals

118

29314.047

248.42

Problem 2

Researchers suspect that greater lead exposure results in lower IQ scores.Based on this, they claim that children in the "low lead" group will have a higher average IQ than children in the "high lead" group.They conduct a hypothesis test at the 5% significance level.

1. (2 points) State the null and alternative hypotheses.
2. (2 points) Are the conditions for inference satisfied?Explain.
3. (2 points) Compute the test statistic.For full credit, be sure to show your work.
4. (2 points) Determine the p-value or the critical value (depending on the method you prefer).Either way, be sure to show your work by drawing a sketch.
5. (2 points) Using either the p-value or critical value method, make a decision about the null hypothesis.
6. (1 point) Based on the results of the hypothesis test, is there convincing evidence that children in the "low lead" group have a higher average IQ than children in the "high lead" group?