##### MS 150 Statistics Spring 2001 Midterm Examination Lee Ling
Statistic Equations Excel
Mean = = x P(x) =AVERAGE(data)
Sample Standard Deviation = sx
=
=STDEV(data)
Population Standard Deviation =
= sx
=STDEVP(data)
Slope =SLOPE(y data, x data)
Intercept =INTERCEPT(y data, x data)
Correlation =CORREL(y data, x data)

Examination note: Numbers 16, 17, 26, and 27 are interpretation and analysis questions.   These should be answered using complete sentences and paragraph structure on a separate sheet of paper.  This examination can be, if you choose, typed up, printed and turned in or submitted by email to dleeling@comfsm.fm .

The test is due Friday morning 10:00 A.M. 02 March 2001.

### I. Descriptive Statistics

The following data gives the number of Liberal Arts/Pre-Nursing students at the College of Micronesia-FSM from 1995 to 2001.  In the first column is the year, with year 0 being 1995 and year being 2001. Note that this is seven years in all.  The first section uses the second column, the y data, to obtain some descriptive statistics.

Year, where 1995 is year 0 (x) Number of students in nursing program (y)
0 44
1 38
2 28
3 20
4 18
5 12
6 3
1. What level of measurement is the number of nursing students y data?

2. _______ What is the mean number of nursing students () for these seven years?

3. _______ What is the median number of nursing students?

4. _______ What is the mode of the number of nursing students?

5. _______ What is the sample standard deviation sy of the number of nursing students?

6. _______ What is the sample Coefficient of Variation of number of nursing students?

### II. Linear Regression

Use the data from Section I to complete this section.

1. Plot the data from section one on the following graph:

2. _______ Calculate the slope of the least squares (best fit) line.

3. _______ Calculate the intercept of the least squares (best fit) line.

4. _______ Using the least squares line equation, what year will the LA/pre-nursing program have zero students?

5. _______ The Pearson product-moment correlation will indicate whether the growth can be reasonably modeled by a linear equation.  What is the correlation r for the data in section I?

6. Is the correlation...
1. perfect negative correlation
2. highly negative correlation
3. moderately negative correlation
4. no correlation
5. moderately positive correlation
6. highly positive correlation
7. perfect positive correlation
7. _______ What is the Coefficient of Determination r² for the data in section I?

8. What does the Coefficient of Determination tell us?

9. _______ Is the rate of change reasonably well modeled by a linear equation?
1. Why?

10. What does the data tell us about the condition of the pre-nursing program at the College? (Use a separate sheet of paper)

11. Think of yourself as an administrator at the College.  Imagine yourself as a chair, director, vice-president, comptroller, or president.  You choose the viewpoint you wish to take.  What recommendations would you make for the pre-nursing program at the College and WHY? (Use a separate sheet of paper)

### III Histograms and Probability Distributions

At the national campus the distribution of grades for pre-nursing majors in courses from 1995 to present is given in the table below. The second row of the table can be read in the following manner: "89 grades of A were awarded to pre-nursing majors between Spring 1995 and Fall 2000."

Grade Grade Point Value (x) Frequency or Count Rel. Freq. or P(x) x P(x) (x-m)²P(x)
A 4 89 » » »
B 3 238 » » »
C 2 346 » » »
D 1 204 » » »
F or W 0 354 » » »

Sums:

» » » »
»
1. Calculate the probability distribution (the relative frequencies) for each grade   and record the results in the table above.
2. Make a histogram of the probability distribution (relative frequency histogram) using the Grade Point Values for the x axis as seen below.
3. What is the shape of the distribution?

4. _______ Based on the data, what is the probability that a randomly selected pre-nursing student will have a grade of "B" in a class in the class?

5. _______ Calculate P(C or D).

6. _______ Calculate the mean of the data.

7. Is the mean above or below the Pell eligibility grade point average requirement?

8. _______ Calculate the standard deviation of the data.

9. What explanations for the trend data presented in section 1 does the grade distribution data suggest? In other words, does the data of section III help explain the trend seen in section I and WHY?  (Use a separate sheet of paper)

10. What suggestions would you make for improving the grade distribution data.  Give me realistic solutions that the College could conceivably implement. (Use a separate sheet of paper)