Description

Assignment Goals:

Each assignment is designed to provide you with an opportunity to demonstrate that you have mastered a portion of the course material.  In this assignment, I hope that you will show that you can:

1.    Enter data using R Commander.

2.    Use R and R Commander to compute some basic descriptive statistics.

3.    Evaluate a research claim based on simple descriptive statistical comparisons.

4.    Use the normal curve characteristics to answer applied research questions.

Assignment:

Professor Schmedlap, a man of limited academic acumen but considerable entrepreneurial interest, has just developed a new and improved reading program.  The professor believes that his reading program would be more marketable if he were to demonstrate that it actually produced better readers.  (As we shall see in this and other assignments, the obvious rarely escapes our good professor; it is the subtleties with which he has problems.)

In order to evaluate the effects of his reading program, Professor Schmedlap administers a standardized norm-referenced reading test to a group of fourteen students before and following implementation of his reading program.  He obtains the following scores on the 100-point test.

          Pretest (x)                                                   Postest (y)

              54                                                                83

              45                                                                86

              67                                                                87

              88                                                            100

              12                                                                50

              77                                                                98

              66                                                                92

                5                                                               88

              79                                                                88

              90                                                                99

              80                                                                95

              55                                                                85

              65                                                                80

              66                                                                86

1.    a.  Calculate the mean, mode, median and range for each set of scores. (10 marks).

list(data_STM.xlsx)

x <-c(5,12,45,54,55,65,66,66,67,77,79,80,88,90)

mean(x)

median(x)

names(table(x))[table(x)==max(table(x))]

range(x)

var(x)

sd(x)

y <-c(50,80,83,85,86,86,87,88,88,92,95,98,99,100)

mean(y)

median(y)

names(table(y))[table(y)==max(table(y))]

range(y)

var(y)

sd(y)

Values for mean, median, mode and range for Pre-test scores are as follows: 60.64

66

66

Min range 5 and Max range 90.

Values for mean, median, mode and range for Post-test scores are as follows: 86.93

87.5

86, 88

Min Range 50 and Max Range 100

b.  Assuming that Professor Schmedlap wishes to compare pre-test and post-test scores, what is the best measure of central tendency for this purpose? Why?  (10 marks).

c.  Calculate the variance and standard deviation for the pre-test and post-test.  (15 marks).

     Values for Variance and Standard deviation for Pre-test scores are as follows: 653.12 and 25.55

     Values for Variance and Standard deviation for Post-test scores are as follows: 151.15 and 12.29

d.  Why is the standard deviation of the post-test scores less than that found in the pre-test?  (15 marks).

e.  Professor Schmedlap is delighted with the results of his study and pronounces that his reading program is the best that is currently available.  Comment on this claim.  (20 marks).