Suppose That X Has a Normal Distribution with Mean 30.2 and Standard Deviation 5.3

STATISTICS 244.3 (01) Term Test 1 May, 2007

Open Book Examination: Students are allowed to take into the examination a calculator, their textbook, and formulae sheets. Each question is worth approximately the same value (2 marks).

Student Name: Student No:

I. In the following study educational researchers were interested in whether a New Method for teaching mathematics was more effective than the Standard Method. A sample of 20 students were taught by the Standard Method, while another sample of 15 students were taught by the New Method. Each student was given a mathematics proficiency test at the end of the teaching period. The scores on this test are tabulated below:

Standard 54.2 61.9 69.2 76.1 55.8 67.3 73.9 67.3 73.9 71.4 Method 76.4 69.6 66.0 81.1 66.6 77.2 89.9 85.4 66.3 67.9 New 77.5 70.3 63.2 33.4 55.6 42.0 13.8 10.7 36.9 71.6 Method 37.9 23.7 14.5 26.6 55.2

Some Summary Statistics are given below: n x x2 Standar 20 1417.4 101932.70 d Method New 15 632.9 33669.55 Method Answer

1. Determine the mean of math proficiency scores of students taught by the Standard E Method. 2. Determine the median of math proficiency scores of students taught by the New H Method. 3. Determine the median of math proficiency scores of students taught by the Standard A Method. 4. Determine the mean of math proficiency scores of students taught by the New F Method. Choices for 1 to 4 a) 69.4 b) 48.0 c) 74.0 d) 16.3 e) 70.9 f) 42.2 g) 29.3 h) 37.9 i) 77.0 j) 62.5

/continued STATISTICS 244.3 Term Test 1

5. Determine the Range of math proficiency scores of students taught by the New C Method. 6. Determine the Pseudo-Standard deviation (PSD) of math proficiency scores of G students taught by the New Method. 7. Determine the Range of math proficiency scores of students taught by the Standard H Method. 8. Determine the Interquartile Range (IQR) of math proficiency scores of students taught J by the New Method. 9. Determine the Pseudo-Standard deviation (PSD) of math proficiency scores of F students taught by the Standard Method. 10. Determine the standard deviation (s) of math proficiency scores of students taught by I the New Method. 11. Determine the Interquartile Range (IQR) of math proficiency scores of students E taught by the Standard Method. 12. Determine the standard deviation (s) of math proficiency scores of students taught by D the Standard Method. Choices for 5 to 12 a) 50.2 b) 14.5 c) 66.80 d) 8.83 e) 9.80 f) 7.26 g) 29.26 h) 35.70 i) 22.31 j) 39.50 D 13. Find the Stem-leaf of math proficiency scores of students taught by the Standard Method. 14. Find the Stem-leaf of math proficiency scores of students taught by the New Method. H Choices for 13 to 14 a) 0 b) 0 c) 0 d) 0 1 1 1 1 2 2 4.5 2 3.3,3.4,4.2,4.7,7.8 2 3 3 0.4,7.2 3 1.8,1.9,2.5,3.4,7.3 3 4 4 1.7,2.1,4.6,6.8,9.0 4 7.1 4 5 6.2 5 4.2,8.7,8.9,9.1 5 5 4.2,5.8 6 3.4,4.5,5.1,7.1,9.2 6 0.2,3.2,6.5 6 1.3,7.7,8.2 6 1.9,6.0,6.3,6.6,7.3,7.3,7.9,9.2,9.6 7 1.1,3.9,4.6,6.0,6.3,7.6,7.7,7.8,8.3,9.0 7 7 9.9 7 1.4,3.9,3.9,6.1,6.4,7.2 8 0.9,1.1,8.6 8 8 8 1.1,5.4,9.9 9 3.6 9 9 9 e) 0 f) 0 g) 0 -0.1 h) 0 1 1 1 7.5 1 0.7,3.8,4.5 2 2 2 4.7 2 3.7,6.6 3 3 3 4.7,5.6 3 3.4,6.9,7.9 4 7.1,8.1,9.9 4 4 7.9,8.9 4 2.0 5 5 0.0,9.3 5 5.5 5 5.2,5.6 6 1.5,2.7,3.1,3.5,5.9,6.3 6 3.8,6.3,6.7,8.8,9.5 6 5.2,5.6,6.9,9.6 6 3.2 7 0.8,0.8,1.2,1.8,4.6,8.9,9.0 7 1.0,2.0,3.4,6.4,6.8,6.8,7.0,7.8,8.7,8.8,8.9,9.3 7 6.4 7 0.3,1.6,7.5 8 0.9,7.2,9.3 8 2.0 8 0.2,0.7 8 9 0.5 9 9 9 STATISTICS 244.3 Term Test 1

II. Consider the data from two samples displayed in the two histograms:

Sample A Sample B

f 15 f 15

0 0 10 to 20 20 to 30 30 to 40 40 to 50 50 to 60 60 to 70 70 to 80 80 to 90 90 to 100 10 to 20 20 to 30 30 to 40 40 to 50 50 to 60 60 to 70 70 to 80 80 to 90 90 to 100 Determine if the following statements are TRUE or FALSE.

15. The median for sample A is larger than the mean for sample A. F

16. The mean for sample B is 65. F

17. The Interquartile range (IQR) for sample B is at least 75. F

18. The median for sample A is smaller than the median for sample B. T

19. Sample A is a negatively skewed distribution. F

20. For Normal distributions the mean and the median are approximately the same T

The End STATISTICS 244.3 Term Test 1