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 1

Before performing any further analysis, researchers wish to determine if there is a statistical difference in average IQ scores between some of the lead levels.

1. (2 points) Write the null and alternative hypotheses for a test to see if there is a difference in average IQ scores between some of the groups.
2. (2 points) Based on an examination of the box plots, do you believe there is a difference in the average IQ scores between some of the groups?Explain.

(2 points) At the 0.05 siResearchers 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 1

Before performing any further analysis, researchers wish to determine if there is a statistical difference in average IQ scores between some of the lead levels.

1. (2 points) Write the null and alternative hypotheses for a test to see if there is a difference in average IQ scores between some of the groups.
2. (2 points) Based on an examination of the box plots, do you believe there is a difference in the average IQ scores between some of the groups?Explain.
3. (2 points) At the 0.05 significance level, can we conclude that there is a difference in average IQ scores between some of the groups?Explain.
4. (2 points) Does the result of the hypothesis test change if we reduce the significance level to 0.01?Explain why or why not.
5. gnificance level, can we conclude that there is a difference in average IQ scores between some of the groups?Explain.
6. (2 points) Does the result of the hypothesis test change if we reduce the significance level to 0.01?Explain why or why not.