18. Do the results indicate a significant difference between blood pressure before and blood pressure after treatment? Use a two-tailed test with α =  .05. To answer this question first find the test statistic and the critical value.  Test statistic = ? Critical value = ? Reject or Retain the null hypothesis? (Enter "Reject" or "Retain")      19. For the test conducted in problem 18, compute r2 to measure the size of any effect. Indicate whether the effect size are small, medium, or large.   r2 =  ,?  r2 is (Enter small, medium, or large): ?

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Author:HOUGHTON MIFFLIN HARCOURT
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Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 14CR
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(For Questions 17-19 and 20-24). The following data was collected from a clinical trial testing a new drug aimed to lower blood pressure for individuals older than age 45. Half of the 20 participants received the new drug (Treatment = Yes) and the other half of the participants received a placebo pill (Treatment = No). Their age and gender was also recorded. Please use this data for Questions 17-19 and 20-24 and note, not all the information in the table will be used for either problem, you must decide what is relevant based on what the problem is asking.

Subject ID

Treatment

Age

Gender

BP_Before

BP_After

D1

Yes

65

F

103.3

80.5

D2

Yes

59

F

93.6

85.9

D3

Yes

60

M

92

85.2

D4

Yes

54

F

93

87.8

D5

Yes

65

F

95.4

85.3

D6

Yes

57

M

109.6

94.2

D7

Yes

69

M

97.9

83.9

D8

Yes

62

M

96

85

D9

Yes

49

F

98.4

86.3

D10

Yes

45

M

98.4

90

C1

No

63

F

97.4

93.1

C2

No

56

F

97.2

92.4

C3

No

54

M

98.8

94.6

C4

No

69

M

98.4

92.3

C5

No

75

M

89.8

89.3

C6

No

62

F

103.4

99.7

C7

No

61

F

90.1

88.4

C8

No

59

M

93.7

90.4

C9

No

73

M

96.4

91.1

C10

No

57

F

98.6

90.5

 

18. Do the results indicate a significant difference between blood pressure before and blood pressure after treatment? Use a two-tailed test with α =  .05. To answer this question first find the test statistic and the critical value. 

Test statistic = ?

Critical value = ?

Reject or Retain the null hypothesis? (Enter "Reject" or "Retain") 

 

 

19.

For the test conducted in problem 18, compute r2 to measure the size of any effect. Indicate whether the effect size are small, medium, or large.

 

r2 =  ,? 

r2 is (Enter small, medium, or large): ?

Expert Solution
Step 1

18.

Let μd is defined as the mean difference between blood pressure before and blood pressure after treatment. The test is that the results indicate a significant difference between blood pressure before and blood pressure after treatment. The hypothesis is,

Null hypothesis:

H0:μd=0

Alternative hypothesis:

H1:μd0

The difference is,

BP_Before BP_After Difference
103.3 80.5 22.8
93.6 85.9 7.7
92 85.2 6.8
93 87.8 5.2
95.4 85.3 10.1
109.6 94.2 15.4
97.9 83.9 14
96 85 11
98.4 86.3 12.1
98.4 90 8.4
97.4 93.1 4.3
97.2 92.4 4.8
98.8 94.6 4.2
98.4 92.3 6.1
89.8 89.3 0.5
103.4 99.7 3.7
90.1 88.4 1.7
93.7 90.4 3.3
96.4 91.1 5.3
98.6 90.5 8.1

The descriptive statistics is conducted using EXCEL. The software procedure is given below:

  • Enter the data.
  • Select Data > Data Analysis >Descriptive Statistics> OK.
  • Enter Input Range as Difference(A1:A21) column.
  • Mark Labels in First Row.
  • Mark Summary Statistics.
  • Click OK.

The output using EXCEL is as follows:

Statistics homework question answer, step 1, image 1

From the output, the mean is 7.775, and the standard deviation is 5.3031.

The test statistic is,

t=x¯d-μdsdn=7.775-05.303120=7.7751.1858=6.5568

Thus, the test statistic is 6.5568.

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