Question

21.HE.B: Captopril is a drug designed to lower systolic blood pressure. When subjects were treated with this drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. The results are in the accompanying table on the next page.

(a)      Go through “The Drill” for paired t-tests (Use a 0.05 α-level and the corresponding confidence interval.)

          The Drill:

• Assumptions and Conditions
  • Paired Data Condition

The data must be paired. Only use pairing if there is a natural matching. The two-sample t-test and the paired t-test are not interchangeable.

Independence Assumption

For paired data, the groups are never independent. Need differences independent, not individuals Randomization ensures independence.

Normal Population Assumption

Need to assume the differences follow a Normal model.

• One or two-sided?
• α-level = 0.05
• Statement of the Hypothesis
• Distribution of the sample mean under Ho.
• Make a picture
• Mechanics – test statistic
• p-value
• Interpretation in context
• Conclusion
• Type I and Type II error

(b)      What p-value do we get if we choose the (incorrect) two-sample test of Chapter 20 instead of the (correct) paired t-test? Will it affect the conclusion?

	A	B	C	D	E	F	G	H	I	J	K	L
Before	200	174	198	170	179	182	193	209	185	155	169	210
After	191	170	177	167	159	151	176	183	159	145	146	177

Answer 1

Paired Data Condition

The data must be paired. Only use pairing if there is a natural matching.

For paired data, the groups are never independent.

Normal Population Assumption

Following table shows the calculations:

Before	After	d=before-after	(d-mean)^2
200	191	9	44.89
174	170	4	2.89
198	177	21	349.69
170	167	3	0.49
179	159	20	313.29
182	151	31	823.69
193	176	17	216.09
209	183	26	561.69
185	159	26	561.69
155	145	10	59.29
169	146	23	428.49
210	177	33	942.49
Total		223	4304.68

Conclusion We cannot conclude that Captopril drug lowers systolic blood pressure..

Since we fail to reject the null hypothesis so type II error is possible.

(B)

Following is the output of independent sample t test:

Hypothesis Test: Independent Groups (t-test, pooled variance)
	Before	After
	185.33	166.75	mean
	17.07	14.86	std. dev.
	12	12	n
		22	df
		18.583	difference (Before - After)
		256.133	pooled variance
		16.004	pooled std. dev.
		6.534	standard error of difference
		0	hypothesized difference
		2.84	t
		.0047	p-value (one-tailed, upper)
	F-test for equality of variance
		291.33	variance: Before
		220.93	variance: After
		1.32	F
		.6544	p-value

So the p-value is: 0.0047

In this we reject the null hypothesis and conclude that Captopril drug lowers systolic blood pressure..