Sample Questions for Exam 3

Note - there are more questions in this sample than there will be in the real exam

Data can be copied directly from this page to Excel

Test significance at alpha = 0.05 unless otherwise indicated.

1. A regression of weight (in kg) on age (in years) for small children generates b = 2.1 and a = 8.2.  What is the expected weight of a child 4 years 3 months old?
   
   
   
   
   
   
   
2. Data on the average IQ of children from different sized families are presented in the Excel spreadsheet.  Use a “hand-calculated” regression to determine the relationship between average IQ and the number of children in the family.  Then calculate the 95% confidence interval for the resulting slope and indicate the values below.

   # of children	Average IQ
   1	105
   2	102
   3	104
   4	100
   5	97
   6	101
   7	95
   8	93
   9	96
   10	88

   
   
   
   
   
   

3. In regression, what statistic indicates the amount of the variation in Y that can be explained by X?
   
   
   
   
   
4. The clutch size for ten individuals of a species of lizard is measured for their first, second and third clutches (data in Excel worksheet). 

   	Clutch
   ID	1	2	3
   1	8	10	8
   2	6	8	14
   3	12	12	10
   4	9	10	10
   5	6	7	5
   6	9	9	7
   7	7	10	7
   8	6	10	6
   9	12	12	13
   10	12	12	9

   
   

   1. Calculate the Pearson’s correlation coefficient for clutches 1 and 2, and for 1 and 3.
      
      
      
      
      
   2. Determine if these two correlation coefficients are significantly different.
      
      
      
      
      
   3. Compare clutches 1 and 2 using a non-parametric method.
      
      
      
      
      
      
      
      
      
      
5. During a stint working for the MCAT grading service, you are asked to ascertain what degree of association, if any, exists between the verbal, physical and biological scores of students.  What approach would you use to determine this?
   
   
   
   
   
   
   
6. Shamelessly looking into sealed medical records, you obtain the below data on age and systolic blood pressure in women.  Your goal is to be able to determine the expected blood pressure for a woman based on her age.  Carry out an appropriate analysis of the data, and use your findings to predict the blood pressure of a 60 year old woman.

   ID	Age	Systolic BP		ID	Age	Systolic BP		ID	Age	Systolic BP
   1	42	130		11	64	155		21	71	158
   2	46	115		12	81	160		22	76	158
   3	42	148		13	41	125		23	44	130
   4	71	100		14	61	150		24	55	144
   5	80	156		15	75	165		25	80	162
   6	74	162		16	53	135		26	63	150
   7	70	151		17	77	153		27	82	160
   8	80	156		18	60	146		28	53	140
   9	85	162		19	82	156		29	65	140
   10	72	158		20	55	150		30	48	130

   
   
   
   
   
   
   

7. A student survey is undertaken to determine whether Chemistry or Biology has better teachers.  Three professors in each department, each of whom teaches three unique courses, are examined. (The names have been changed to avoid litigation). For each course, a mean score of student satisfaction is taken - data are shown below.  Test the question posed using an appropriate method.

   Chemistry		Biology
   Instructor	Ratings	Instructor	Ratings
   Dr. Benzene	3.9, 3.2, 4.1	Dr. Golgi Body	4.2, 4.5, 3.9
   Dr. Enthalpy	4.2, 4.4, 4.0	Dr. Adipose Tissue	4.8, 4.6, 4.4
   Dr. Homonuclear Diatomic Molecule	3.8, 3.6, 4.2	Dr. Displacement Behavoir	4.0, 4.3, 4.1

   
   
   
   
   
   
   
   
   
8. Recall the question below from a previous practice exam. Analyze the data again, this time using a non-parametric approach.
   
   You want to determine whether a certain hormone affects growth rates in mammals. Using mice as a model organism, you take two siblings from each of 6 litters of mice, and in each case inject one sibling with the hormone and the other with a placebo. You then weigh the mice two weeks later. The resulting data are below.

   Litter	Hormone	Placebo
   A	3.6	5.2
   B	3.6	5.5
   C	4.4	4.0
   D	3.7	4.6
   E	4.8	5.3
   F	3.6	3.8

   
   
   
   
   
   
9. Again, recall the question below from a previous practice exam. Analyze the data again, this time using a non-parametric approach.
   
   You develop a new nutritional supplement for pregnant women and run an experiment to test its effectiveness.  You convince 10 expectant mothers to try the supplement, and they have babies with the birth weights shown below.  You also know that U.S. birth weights have a median value of 3.4 kg. Does the sample differ significantly from this value?

   Observed birth weights: 2.9, 3.0, 2.7, 3.7, 2.6, 3.2, 3.1, 2.7, 2.8, 3.5 kg

   
   
   
   
   
10. A study is undertaken to examine the possible benefits of two different vitamin regimens on growth in infants.  Seven sets of triplets are used for the study, with each child of a given family receiving one of the two regimens or no supplement.  Weight gain is then measured over the next two years (data below).  Determine whether either of the vitamin treatments is useful using a non-parametric test.

    Family	No supplement	Regimen 1	Regimen 2
    A	11.2	9.3	10.4
    B	9.7	12.0	11.5
    C	8.2	9.4	8.9
    D	9.1	10.1	7.9
    E	11.0	10.3	10.8
    F	7.3	9.1	8.4
    G	8.2	8.3	10.1