Question

Problem 2: The element mercury causes massive brain dysfunction, including hallucinations and delusions. Also, a "silver filling" from your dentist is actually 50-66% mercury and only 35% silver. The American Dentistry Association (ADA) says that silver amalgams are safe because the mercury is not relased. However, mercury can be measured in your hair and your urine because the mercury is apparently released by chewing. The ADA says this amount is not bothersome. A statistician for a company that produces filling compounds wishes to determine whether mercury fillings affect a child's brain functioning. A MBD (minimal brain dysfunction) parental survey-test is created which has 20 questions about MBD symptoms like "My child has learning problems," "My child is hyperactive," etc. The overall score on the MBD test ranges from 0 (no evlduence of brain dysfunction) to 20 (severe brain dysfunction). The survey is given to parents as they visit a dentist with their child. The number of silver fillings is noted, as is the child's gender. For analysis purposes, the children are divided up into whether they have no fillings, one to three fillings, or more than five fillings, and their MBD scores is noted.


Male - No Fillings: 7, 4, 6, 7, 8, 5, 9, 5
Female - No Fillings: 4, 6, 7, 8, 4, 3, 7, 9
Male - 1 to 3 Fillings: 11, 12, 10, 9, 13, 14, 15, 10
Female - 1 to 3 Fillings: 6, 9, 9, 9, 8, 5, 7, 5
Male - 5+ Fillings: 17, 20, 15, 17, 16, 14, 18, 20
Female - 5+ Fillings: 13, 15, 11, 12, 10, 12, 14, 14

1) The sum of squares for gender are

a) 615.13

b) 935.31

c) 157.63

d) 117.19

2) The sum of squares for fillings in Problem 2 are

a) 615.13

b) 935.31

c) 157.63

d) 117.19

3) The sum of squares for the interaction in Problem 2 are

a) 45.38

b) 935.31

c) 157.63

d) 615.13

4) The error term sum of squares for Problem 2 are

a) 45.38

b) 935.31

c) 157.63

d) 615.13

5) The degrees of freedom for gender in Problem 2 are

a) 1

b) 2

c) 42

d) 47

6) The degrees of freedom for fillings in Problem 2 are

a) 1

b) 2

c) 42

d) 47

7) The degrees of freedom for interaction in Problem 2 are

a) 1

b) 2

c) 42

d) 47

8) The F value for gender in Problem 2 is

a) 6.045

b) 31.225

c) 81.952

d) 1.000

9) The F value for fillings in Problem 2 is

a) 6.045

b) 31.225

c) 81.952

d) 1.000

10) The F value for the interaction in Problem 2 is

a) 6.045

b) 31.225

c) 81.952

d) 1.000

Answer 1

Applying 2 way ANOVA (With replication) from excel: data-data analysis

Source of Variation	SS	df	MS	F	P-value	F crit
Gender	117.19	1	117.19	31.23	0.0000	4.07
Fillings	615.13	2	307.56	81.95	0.0000	3.22
Interaction	45.38	2	22.69	6.05	0.0049	3.22
Within	157.63	42	3.75
Total	935.31	47

1) sum of squares for gender are =117.19

2) sum of squares for fillings in Problem 2 =615.13

3) The sum of squares for the interaction in Problem 2 =45.38

4) The error term sum of squares for Problem 2 =157.63

5) The degrees of freedom for gender in Problem 2 =1

6) degrees of freedom for fillings in Problem 2 =2

7) degrees of freedom for interaction in Problem 2 =2

8) F value for gender in Problem 2 =31.225

9) F value for fillings in Problem 2 =81.952

10) e F value for the interaction in Problem 2 is =6.045