Statistics and Probability Answers

Mr. Ali wishes to determine if there is a significant difference in the learning abilities of the students in Statistics. He randomly selected 10 students and the following information were gathered:

Students

1

2

3

4

5

6

7

8

9

10

Pretest Scores

23

22

26

29

31

34

37

40

31

37

Posttest Scores

26

25

28

31

30

42

39

40

45

40

2. A manufacturing firm claims that the average income of their employees per day is 360 Php. A random sample of 25 employees were tested and found to have a mean daily income of 325 Php with a standard deviation of 3.6. Test the hypothesis that = 360 against the alternative < 360 using 0.05 level of significance.

A vicious debate between behaviorists and traditional medical doctors concerns the merits of using the stimulant Ritalin in treating childhood hyperactivity. A large group of hyperactive children in an urban school system were randomly assigned to either a behavior modification program or a drug therapy program. The dependent variable measured is the children’s' hyperactivity score after 18 weeks of treatment. Use the data shown directly below to determine if there is a significant difference on these children’s' hyperactivity scores.

Behavior

22

24

27

18

21

19

18

17

14

17

20

16

13

20

16

12

14

22

23

18

Drug

26

32

31

20

34

36

22

29

27

25

24

32

24

20

32

32

29

27

33

30

Diagnosing stroke strictly on the basis of clinical symptoms is difficult. A standard diagnostic test used in clinical medicine to detect stroke in patients is the angiogram. This test has some risks for the patient, and researchers have developed several noninvasive techniques that they hope will be as effective as the angiogram. One such method measures cerebral blood flow (CBF) in the brain because stroke patients tend to have lower CBF levels than normal. Assume that in the general population, CBF is normally distributed with mean =751 mL / 100 brain tissue and standard deviation =17 mL/100 g brain tissue. A patient is classified as being at risk for stroke if his or her CBF is lower than 40mL / 100 g brain tissue.

What proportion of normal patients will be mistakenly classified as being at risk for stroke?