HYPOTHESIS TESTING SINGLE POPULATION MEAN

1. Super Duper Cee Pills were advertised as having 750 mg of vitamin C per pill. A consumers group believed the amount of vitamin C was less than advertised. Based on the following sample, was this advertisement justified? Use

700755760

720720725

760720720

780730695

710740715

2. A researcher wanted to determine whether a program for routine cholesterol screening of college men would identify high serum cholesterol levels. The researcher decided that above 200 would be high. Twenty students were randomly selected for cholesterol screening, and the results were given below. Is there any evidence that asymptomatic college men have elevated serum cholesterol values? Would a large-scale screening program be warranted? Use

260210240230260

150220190210240

160220250180200

200210170250220

asymptomatic[yssimpt mttik]

adjective

without obvious symptoms: not showing or producing indications of a disease or other medical condition

The operation was successful, and she has remained asymptomatic ever since.

Microsoft Encarta Premium Suite 2005. 1993-2004 Microsoft Corporation. All rights reserved.

3. In one part of a test developed by a psychologist, the test subject is asked to form a word by unscrambling the letters ciiatttsss. (Try it yourself). Given below are the times (in seconds) required by 15 randomly selected persons to unscramble the letters. At level of significance, test the claim that the mean time is equal to 60 seconds.

Data set:

68.783.739.5

68.626.034.6

43.443.685.3

27.468.961.1

48.460.526.3

4. The HRD head observes that absenteeism is high in graveyard shift than in the morning shift. The daily time record of the employees shows the number of their absences for a period of two weeks.

Morning shift

2343212

4465312

Graveyard shift

3335563

2435543

5. Twelve different tablets from each of the two competing cold medicines are randomly selected and tested for the amount of acetaminophen each contains, and the results (in milligrams follow)

Dozenol

472

487

506

512

489

503

511

501

495

504

494

462

Niteze

562

512

523

528

554

513

516

510

524

510

524

508

At 0.05 level of significance, test the claim that the mean amount of acetaminophen is the same in each brand.

6. It is claimed that the new diet will reduce a persons weight by 4.5 kilograms on the average in a period of 2 weeks. The weights of 7 women who followed this diet were recorded before and after a two-week period:

woman

1

2

3

4

5

6

7

Weight before

58.5

60.3

61.7

69.0

64.0

62.6

56.7

Weight after

60.0

54.9

58.1

62.1

58.5

59.9

54.4

At 0.05 level of significance, test if the new diet is really effective?

7. A teacher proposes a course designed to increase the reading speed and comprehension. To evaluate the effectiveness of this course, the teacher tests students before and after the course. Test the claim that the course is effective.

Data: reading speed/time (in seconds)

student

before

After

1

100

136

2

170

160

3

135

120

4

167

169

5

200

200

6

118

140

7

127

163

8

95

101

9

112

138

10

136

129

8. A study was conducted to investigate some effects of physical training. At 0.05 level of significance, test the claim that the mean pre-training weight equals the mean post-training weight. The weights are in kilograms. What do you conclude about the effect of training on weight?

Pre-training weight

Post-training weight

99

94

57

57

62

62

69

69

74

66

77

76

59

58

92

88

70

70

85

84

9. A dose of the drug Captropil, designed to lower systolic blood pressure, is administered to 10 randomly selected volunteers, with the following results. Test the effectiveness of the drug

systolic blood pressure before pill

systolic blood pressure after pill

120

118

136

122

160

143

98

105

115

98

110

98

180

180

190

175

138

105

128

112

10. An experiment in teaching introductory statistics was recently conducted at XYZ University. One section was taught by demonstration method and another section was taught by videotaped lecture where the students are free to view at any time and as often as they wanted. Students were randomly assigned to each of the two sections and an achievement test was given at the end of the treatment. Random test scores were collected from each section. Is there a significant difference in the student performance given different teaching methods?

videotape

Demonstration

37

27

30

24

26

22

31

19

29

20

32

20

19

23

37

14

28

15

26

13

11. Per capita expenditures for police protection for 30 cities are reported for 1999 and 2000. Is there a significant increase in the per capita expenditures for policemen?

Year 1999

Year 2000

180

210

95

110

87

124

101

131

52

197

117

200

115

119

88

87

85

125

100

150

167

225

101

209

120

201

78

141

107

94

55

248

78

140

92

131

99

152

103

178

98

150

65

160

102

170

110

150

98

100

95

112

97

120

110

114

120

98

121

162

12. The table below shows the salaries of three groups of employees as high school graduate, college graduate, and post graduate. The salaries are presented in the table below. Figures are in thousand pesos.

High School Graduate

15

16

18

21

18

17

College Graduate

16

19

28

24

28

30

31

21

27

Post Graduate

17

24

27

20

31

30

30

32

31

35

13. A medical researcher wishes to know whether there is a difference in the mean length of time it takes the four types of medicines to take effect and provide relief for a person suffering from fever

Medicine A

10

11

15

12

Medicine B

10

15

20

25

16

Medicine C

14

19

25

26

18

Medicine D

20

15

17

12

19

20

Is there difference in the mean length of time? Use the 0.05 level of significance

14. A teacher wants to find out whether academic performance is independent of the type of school a student graduated from. He sampled 150 students and results are shown below. At the 0.05 level of significance, can the teacher say that there is a relationship between academic performance and type of school?

Academic performance

Type of school

Public

Private

Total

Excellent

Very good

Good

Fair

Poor

18

15

16

14

15

20

12

19

13

8

38

27

35

27

23

Total

78

72

150

15. A gym instructor wants to determine whether age of a person has something to do with the number of days that such person engages into exercise. A random sample of 264 persons is selected and the results are classified and tabulated below:

At the 0.05 significance level, is there enough evidence to conclude that age is related to the number of days spent exercising per week?

Age

Days per week spent exercising

0-1

2-3

4-5

6-7

Total

Below 18

19-30

31-42

43-54

55 and above

7

6

8

18

8

8

25

9

12

6

10

35

20

13

6

11

20

30

7

5

36

86

67

50

25

Total

47

60

84

73

264