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Biostatistics Practical Revision
Answered

Example 1: Comparing Attractiveness of Psychology Undergrads at CSUN and UCLA

Biostatistics Practical Revision

Example Problems:

�Example 1: A couple of male grad students met at the annual American Psychological Association conference last year, one of them was a grad student from CSUN and the other was a grad student at UCLA. After a short period, they began discussing the joys of going to school in southern California and after a few drinks the conversation quickly turned into an argument about which school CSUN or UCLA had a more attractive psychology undergraduate female population. The CSUN grad argued that CSUN undergraduate females in psychology at CSUN are more attractive and the UCLA grad argued that the UCLA undergraduate females in psych are more attractive. So as graduate students they decided to use their research abilities and answer the questions scientifically. They both randomly selected 35 undergraduate female psych students and asked them if they were willing to participate. Of the 35 solicited from each school, 33 agreed to participate from UCLA and 30 from CSUN. Each participant�s photo was shown to a panel of judges and the average score (out of 10) is shown for each participant in the table below. Which school has the more attractive psychology undergrad population?

Subject

Rating

Subject

Rating

1

4

1

8

2

6

2

7

3

6

3

7

4

8

4

8

5

3

5

5

6

3

6

6

7

7

7

6

8

4

8

6

9

3

9

7

10

5

10

9

11

7

11

7

12

6

12

8

13

8

13

6

14

6

14

7

15

8

15

6

16

4

16

8

17

3

17

7

18

5

18

7

19

7

19

8

20

3

20

7

21

6

21

8

22

4

22

9

23

6

23

8

24

3

24

7

25

5

25

8

26

2

26

7

27

4

27

6

28

6

28

7

29

5

29

7

30

7

30

7

31

4

�

32

2

�

33

3

�

�

Example 2: A cognitive psychologist was reminiscing about graduate school and remembers that he probably would have never made it through had it not been for �energy drinks� like Monster. Many endless nights of writing, reading or both were followed by long days of classes, running subjects and more reading, and writing and it was drinks like Monster energy drink that kept him from crashing. As he thought more about it, it seemed that Monster helped him more than most of his classmates who drank coffee. Sure, they were awake, but their cognitive abilities always seemed a little more taxed than his or other folks� that drank Monster. To test this hypothesis, he randomly selected 24 students and had them �pull an all-night�, he than randomly assigned them to either drink coffee or Monster. He tested their cognitive ability using the CSB (cognitive skills battery), which is known to have a normal distribution in the population, and the results are shown in the table below. Does drinking Monster lead to higher cognitive functioning after a night of little or no sleep when compared to coffee?

Coffee

Monster

Subject

Score

Subject

Score

1

30

1

35

2

42

2

50

3

27

3

51

4

37

4

53

5

31

5

55

6

28

6

63

7

30

7

45

8

36

8

53

9

42

9

50

10

39

10

44

11

51

11

71

12

38

12

47

�

Example 3: An assertiveness training course has just been added to the services offered by a counseling center. To measure its effectiveness, ten students are given a test at the beginning of the course and again at the end. A high score on the test implies high assertiveness. Do the data provide sufficient evidence to conclude that people are more assertive after taking the course?

Example 2: Comparing Cognitive Functioning After Drinking Coffee or Energy Drinks

Before Course������� After Course

50 ����������������������� �65

62 ����������������������� �68

51 ����������������������� �52

41 ����������������������� �43

63 ����������������������� �60

56 ����������������������� �70

49 ����������������������� �48

67 ����������������������� �69

42 ����������������������� �53

57 ����������������������� �61

�Example 4: Twelve cars were equipped with radial tires and driven over a test course. Then the same 12 cars (with the same drivers) were equipped with regular belted tires and driven over the same course. After each run, the cars� gas economy (km/l) was measured. Is there evidence that radial tires produce better fuel economy?

Cars������� | �1 ���2 ���3 ���4 ���5 ���6 ���7 ���8 ���9 ��10 �11 �12

(radial)�� | 4.2 4.7 6.6 7.0 6.7 4.5 5.7 6.0 7.4 4.9 6.1 5.2

(belted)�� | 4.1 4.9 6.2 6.9 6.8 4.4 5.7 5.8 6.9 4.7 6.0 4.9

Example 5: Suppose we want to know whether three different exam prep programs lead to different mean scores on a certain exam. To test this, we recruit�30 students to participate in a study and split them into three groups. The students in each group are randomly assigned to use one of the three exam prep programs for the next three weeks to prepare for an exam. At the end of the three weeks, all of the students take the same exam. The exam scores for each group are shown below:

exam scores

Example 6: Calcium is an essential mineral that regulates the heart, is important for blood clotting and for building healthy bones. The National Osteoporosis Foundation recommends a daily calcium intake of 1000-1200 mg/day for adult men and women. While calcium is contained in some foods, most adults do not get enough calcium in their diets and take supplements. Unfortunately, some of the supplements have side effects such as gastric distress, making them difficult for some patients to take on a regular basis. �

A study is designed to test whether there is a difference in mean daily calcium intake in adults with normal bone density, adults with osteopenia (a low bone density which may lead to osteoporosis) and adults with osteoporosis. Adults 60 years of age with normal bone density, osteopenia and osteoporosis are selected at random from hospital records and invited to participate in the study. Each participant's daily calcium intake is measured based on reported food intake and supplements. The data are shown below. ��

Normal Bone Density

Osteopenia

Osteoporosis

1200

1000

890

1000

1100

650

980

700

1100

900

800

900

750

500

400

800

700

350

�

Is there a statistically significant difference in mean calcium intake in patients with normal bone density as compared to patients with osteopenia and osteoporosis?

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