STATISTICS

Statistics

Task 1: (30 marks)

A student measured the data in the tables below by recording the time, t; it took two different cylinders (one solid and one hollow) with the same dimensions to roll, from rest, down a slope for a fixed distance.

Theory suggests that the hollow cylinder should take longer to travel the same distance as the solid cylinder.

Solution:

Part A)

Frequencies

Statistics

Rolling time for hollow cylinder/sec

Rolling time for solid cylinder/sec

Rolling time for hollow cylinder/sec (Binned)

Rolling time for solid cylinder/sec (Binned)

N

Valid

45

45

45

45

Missing

0

0

0

0

Mean

2.0529

1.8049

4.00

3.84

Std. Deviation

.04586

.06247

.000

.796

Frequency Distribution

Rolling time for hollow cylinder/sec

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

1.97

2

4.4

4.4

4.4

1.98

1

2.2

2.2

6.7

1.99

2

4.4

4.4

11.1

2

2

4.4

4.4

15.6

2.01

3

6.7

6.7

22.2

2.02

3

6.7

6.7

28.9

2.03

5

11.1

11.1

40.0

2.04

2

4.4

4.4

44.4

2.05

3

6.7

6.7

51.1

2.06

3

6.7

6.7

57.8

2.07

6

13.3

13.3

71.1

2.08

3

6.7

6.7

77.8

2.1

3

6.7

6.7

84.4

2.11

2

4.4

4.4

88.9

2.12

3

6.7

6.7

95.6

2.13

1

2.2

2.2

97.8

2.16

1

2.2

2.2

100.0

Total

45

100.0

100.0

Rolling time for solid cylinder/sec

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

1.62

1

2.2

2.2

2.2

1.67

1

2.2

2.2

4.4

1.72

1

2.2

2.2

6.7

1.73

2

4.4

4.4

11.1

1.74

2

4.4

4.4

15.6

1.76

2

4.4

4.4

20.0

1.77

5

11.1

11.1

31.1

1.78

2

4.4

4.4

35.6

1.79

4

8.9

8.9

44.4

1.8

3

6.7

6.7

51.1

1.81

4

8.9

8.9

60.0

1.82

2

4.4

4.4

64.4

1.83

1

2.2

2.2

66.7

1.84

4

8.9

8.9

75.6

1.85

1

2.2

2.2

77.8

1.86

1

2.2

2.2

80.0

1.87

4

8.9

8.9

88.9

1.88

1

2.2

2.2

91.1

1.89

1

2.2

2.2

93.3

1.9

2

4.4

4.4

97.8

1.95

1

2.2

2.2

100.0

Total

45

100.0

100.0

Rolling time for hollow cylinder/sec (Binned)

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

1.95 - 2.16

45

100.0

100.0

100.0

Rolling time for solid cylinder/sec (Binned)

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

1.61 - 1.69

2

4.4

4.4

4.4

1.70 - 1.77

12

26.7

26.7

31.1

1.78 - 1.86

22

48.9

48.9

80.0

1.87+

9

20.0

20.0

100.0

Total

45

100.0

100.0

Part B)

Histogram

Part D)

Standard Deviation of Rolling time for Hollow cylinder

0.05

Standard Deviation of Rolling time for Solid cylinder

0.06



Part E)

Compare Means

Ho: Hollow cylinder should not take longer to travel the same distance as the solid cylinder.

H1: Hollow cylinder should take longer to travel the same distance as the solid cylinder.

The methodology used to test this hypothesis is one-sample T test at the 95% level of confidence.

The test results are as follows;

One-Sample Statistics

N

Mean

Std. Deviation

Std. Error Mean

Rolling time for hollow cylinder/sec

45

2.0529

.04586

.00684

Rolling time for solid cylinder/sec

45

1.8049

.06247

.00931

One-Sample Test

Test Value = 0

t

df

Sig. (2-tailed)

Mean Difference

95% Confidence Interval of the Difference

Lower

Upper

Rolling time for hollow cylinder/sec

300.310

44

.000

2.05289

2.0391

2.0667

Rolling time for solid cylinder/sec

193.806

44

.000

1.80489

1.7861

1.8237

Interpretations

The means of both the samples are different and the significant value of the test is less than the 5% level of significance. Therefore the null hypothesis is rejected.

It is concluded that Hollow cylinder should take longer to travel the same distance as the solid cylinder.

Task 2: (20 marks)

Use the “SDF results data” excel file to answer this question.

The data file shows the module results for 100 SDF students and includes the intended degree route of the students, marks gained in each module and an overall attendance figure; all data in the table is given as percentages.

The following criteria are applied to find the overall grade for the course: Grade

Criteria

Pass with Distinction

Pass all modules with = 40% and gain a mean mark of = 70% across all modules

Pass

Pass all modules with = 40%

Refer

Fail no more than 2 modules with a mark < 40%

Repeat Year

Fail no more than 3 modules with a mark < 40%

Fail no Repeat

Fail more than 3 modules with a mark < 40%

Solution

Part A)

Task 2 & 3 Data - SDF Marks for 100 Students

Module Marks as %

Student

DEGREE

BioA

BioB

ChemA

ChemB

Math

SX0010

Attendance %

1

Pharmaceutical Science

44

44

77

74

78

72

57

Pass

2

Pharmacy

1

3

10

1

5

20

35

Fail No Repeat

3

Forensic Science & Investigative Analysis

60

64

85

89

85

81

81

Pass

4

Pharmaceutical Science or Pharmacology

50

51

79

71

76

75

97

Pass

5

Pharmaceutical Science or Pharmacology

55

55

73

67

41

84

87

Pass

6

Pharmaceutical Science

37

34

57

50

34

79

76

Repeat Year

7

Pharmaceutical Science

58

57

71

70

60

74

87

Pass

8

Pharmacy

71

70

84

80

88

83

90

Pass with Distinction

9

Biomedical Science

34

43

44

33

53

15

35

Repeat Year

10

Pharmaceutical Science

71

71

84

81

74

66

95

Pass

11

Biomedical Science

33

38

51

47

43

51

88

Refer

12

Criminology & Forensic Science

58

55

76

66

58

74

91

Pass

13

Forensic Science & Investigative Analysis

51

46

75

72

45

64

62

Pass

14

Pharmaceutical Science or Pharmacology

35

30

32

34

27

72

55

Fail No Repeat

15

Nutrition

25

30

47

34

22

55

95

Fail No Repeat

16

Biomedical Science

46

40

63

51

48

56

83

Pass

17

Biomedical Science

48

43

46

45

19

62

80

Refer

18

Human Biology & Psychology

16

11

12

7

0

16

50

Fail No Repeat

19

Pharmacy

57

60

85

79

71

86

88

Pass

20

Biomedical Science

7

12

43

34

2

43

45

Fail No Repeat

21

Chemistry

42

32

35

30

33

72

46

Fail No Repeat

22

Pharmaceutical Science or Pharmacology

40

33

67

57

69

74

97

Refer

23

Pharmaceutical Science

42

36

67

71

34

57

51

Refer

24

Pharmaceutical Science

70

64

75

76

57

78

78

Pass

25

Biomedical Science

38

37

58

47

41

72

82

Refer

26

Biomedical Science

74

81

89

88

88

85

93

Pass with Distinction

27

Nutrition

59

60

68

60

54

80

91

Pass

28

Forensic Science & Investigative Analysis

70

60

74

70

41

83

75

Pass

29

Pharmaceutical Science with Industrial Experience

43

34

61

42

22

26

75

Repeat Year

30

Medicinal Chemistry

50

50

63

42

41

81

85

Pass

31

Biomedical Science

27

24

43

23

14

56

60

Fail No Repeat

32

Biomedical Science

10

7

6

4

2

21

32

Fail No Repeat

33

Pharmacy

68

67

85

78

84

81

90

Pass

34

Forensic Chemistry

42

40

73

70

73

82

65

Pass

35

Biochemistry

0

0

0

0

0

8

4

Fail No Repeat

36

Pharmacy

0

10

0

0

22

24

31

Fail No Repeat

37

Pharmaceutical Science or Pharmacology

22

25

36

34

35

70

95

Fail No Repeat

38

Forensic Science & Investigative Analysis

63

70

78

72

45

85

92

Pass

39

Nutrition

61

74

84

78

78

83

95

Pass

40

Biomedical Science

26

38

38

40

58

37

52

Fail ...