

TakeHome Final Exam, due Saturday, April 26, 2003, 9:00 AM
Instructor: Prof. Ivo Dinov  http://www.stat.ucla.edu/~dinov/ 
1. We wish to compare the marriage counselors from two different
clinics with regard to how often couples they have counseled seek a divorce.
As many as possible of the couples counseled by each of the counselors
are located. The following are the percentages for each counselor
of client couples who obtained, or were seeking, a divorce one year after
termination of counseling:
University Clinic  62  32  21 

Mental Health Associates  43  32  27  35 
2. Suppose the gasoline mileages of compact cars for LA driving are normally distributed with mean of 27.1 mpg and standard deviation of 2.3 mpg. What proportion of drivers have a less than 23 mpg? Less than 30 mpg? Between 25 and 30 mpg? What is the mileage that the bottom 10% of the most economical vehicles get? Draw proper graphs/regionsofinterest for all cases.
3. For each
of the following sets of scores, find the mode, the median, and the mean.
Draw boxandwhisker plots. Report the 5number summaries. Would normal assumptions
be valid for any of these data? Would these be considered equalvariance
samples? Why is this important? Do the data histograms. Are these data skewed?
Data 1  12  10  8  19  8  7  13  2  19  9  20  2  17 
Data 2  14  12  17  23  45  60  0  17  2  7  23  18  67  100 
Data 3  11  6  10  11  11  11  9  9  10  10  10  1  7  7 
4. Suppose I selected a random sample of 15 out of the 129
IQ scores of a group of juvenile delinquencies at one juvenile correction
facility in LA. These scores are listed below are the only information you
are given:
89  76  87  43  99  79  92  84  77  96  100  91  89  71  88 
We need to use the sample data to construct a 95% confidence interval for the mean IQ score for this specific population. State the parameter of interest (using a symbol and in words). State the estimate of this parameter (using a symbol, in words and as a number). Calculate SE(parameter). Explain what it means. Clearly interpret your results. Does the confidence interval contain the true mean midterm score for the class? Why?
 A highly significant test result means that the size of the difference between the estimated value of the parameter and the hypothesized value of the parameter is significant in a practical sense.
 A Pvalue of less than 0.01 is often referred to as a weak evidence against the null hypothesis.
 A non significant test result does not necessarily mean H_{o} is true.
 A twotail test of H_{o}: μ = μ_{o} is significant at the 5% significance level if and only if μ_{o } lies outside a 95% confidence interval for μ.
6. A quality control engineer at the Educational Testing Service (ETS) monitors the automatic exam grading for over 12 million multiplechoice "scantron" papers. Each month, to assess fairness and consistency in grading the exams, the engineer takes a random sample of papers, which are then manually graded and the results are compared to the scores obtained by the scanners. For the 12 months of 2002 the following discrepancies between the manual an automated grading methods were observed:
2  4  5  5  6  8  9  10  10  11  12  12 
Suppose the tolerable expected error rate is 1% and the actual number of mannually graded papers in the i^{th} month is i*100, 1 ≤ i ≤ 12. Is there any evidence that the observed discrepancies are purely just due to chance? Or is there a factor whose presence alters the amount of discrepancies? What are the observed and expected discrepancies? Show your work and validate is by using the SOCR resource. Interpret the results.
7. Fill in the blanks:
8. Identify which statements are correct/incorrect. Explain!
TheronP Group:  1.1  1.5  1.6  1.3  0.9  
Control Group:  2.0  1.8  1.4  2.2  1.6  1.6 
Program L  3  7 
Program M  4  10 
Program N  6  12 
Pair Index  1  2  3  4  5  6  7  8  9 
Son  73  68  66  70  74  68  65  72  69 
Father  71  69  63  70  72  69  63  68  70 
Sociability Scale  30  34  35  36  39  39  40  40  42  46 
Peer Ratings of Sociability  72  70  76  80  73  79  76  83  85  81 