Question

In: Statistics and Probability

A clinical trial is conducted to test a new medication designed to lower systolic blood pressure...

A clinical trial is conducted to test a new medication designed to lower systolic blood pressure (SBP). Participants are randomly assigned to receive the new medication or a placebo. The outcome is clinically significant SBP reduction after 30 days. The data are shown below. Compute the totals.

	Significant Reduction in SBP	No Significant Reduction in SBP	Total
New Medication	44	76
Placebo	21	99
Total

Compute the proportion of participants who experienced a significant reduction in SBP, given they received the new medication
1. 0.3667
2. 0.6769
3. 0. 6333
4. 0.175
5. Some other answer (indicate):

Compute the proportion of participants who experienced a significant reduction in SBP, given they received the placebo
1. 0.825
2. 0.3667
3. 0.3231
4. 0.175
5. Some other answer (indicate):

Generate a 90% confident interval for the true proportion of people experiencing a significant reduction in SBP given they received the new medication.
1. (0.3635, 0.3699)
2. (0.2943, 0.4391)
3. (0.3155, 0.4179)
4. (0.2684, 0.465)
5. Some other answer (indicate):

Solutions

Expert Solution

Given,

	Significant Reduction in SBP	No Significant Reduction in SBP	Total
New Medication	44	76	120
Placebo	21	99	120
Total	65	175	240

a. Compute the proportion of participants who experienced a significant reduction in SBP, given they received the new medication

Proportion of Participants who experienced significant reduction in SBP, given they received the new medication

= Number of Participants who received the new medication and experienced significant reduction in SBP / Number of Participants who received the new medication

= 44/120 = 0.3667

Ans : a. 0.3667

b. Compute the proportion of participants who experienced a significant reduction in SBP, given they received the placebo

Proportion of Participants who experienced significant reduction in SBP, given they received the the placebo

= Number of Participants who received the the placebo and experienced significant reduction in SBP / Number of Participants who received the the placebo

= 21/120 = 0.175

Ans : d. 0.175

c. Generate a 90% confident interval for the true proportion of people experiencing a significant reduction in SBP given they received the new medication

Confidence interval for true proportion :

n : sample size : Number of Participants who received the new medication = 120

Sample proportion of participants who experienced significant reduction in SBP, given they received the new medication

= Number of Participants who received the new medication and experienced significant reduction in SBP / Number of Participants who received the new medication

= 44/120 = 0.3667

Confidence Level	90%
(= 100-90/100=10/100 ) = 0.1	0.1
/2 (=0.1/2=0.05)	0.05
	1.6449

90% confident interval for the true proportion of people experiencing a significant reduction in SBP given they received the new medication

90% confident interval for the true proportion of people experiencing a significant reduction in SBP given they received the new medication = (0.2943, 0.4391)

Ans : b. (0.2943, 0.4391)

orchestra answered 1 year ago

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