The following IQ data has been obtained for 12 incoming graduate students:

X: 120 130 132 139 160 115 120 142 148 120 141 135

1. What is the range of this sample?

2. Show a frequency table and a histogram with four to five equal intervals.

3. Compute the mean and standard deviation for this sample.

4. Convert each of the raw scores to Z scores using the sample data.

5. The IQ test, where these scores were derived, follows a normal distribution with a mean of 100 and a standard deviation of 15. Convert each of the raw scores to Z scores using the populational data. Compare the Z scores for the sample data and the populational data. Are they the same or different? Why or why not?

The same students in order above also had provided GPA data after one year of graduate study:

Y: 2.50 3.10 2.75 2.25 3.40 3.25 2.75 3.00 3.15 3.60 3.20 3.00

6. Compute the mean and standard deviation for the GPA distribution above (Y data).

7. Convert each of the Y raw scores into Z scores. Compare the Z scores for the sample IQ data above to the Z scores for the GPA data for each student. How does each student=s Z score compare in the two distributions.

8. Using the X (IQ) & the Y (GPA) data, compute the Pearson=s correlation coefficient (show a table for your calculations). Is there a relationship? What kind of relationship? How strong? Explain the relationship between the two variables, if any.

9. Using regression formula #1 on the formula sheet, calculate the regression equation for the two variables, X (IQ) and Y (GPA). Interpret the significance of the slope constant and the Y-intercept in the regression equation.

10. Using the regression equation, compute the predicted Y= (GPA) value obtained for each X (IQ) value (put data into a table).

11. If you were an admission officer looking at this data relationship and you were interested in students who would succeed at your graduate school, what IQ score cut-off policy would you institute for admission decisions to insure adequate academic performance of your students at your school. Explain how you chose where to make the admission cut based on IQ scores. What minimum GPA would your IQ cut-off score predict?

Please show working. Thanks