When subjects were treated with a drug, their systolic blood pressure readings (
ID: 3158250 • Letter: W
Question
When subjects were treated with a drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. Results are given in the table below. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Using a 0.05 significance level, is there sufficient evidencee to support the claim that the drug is effective in lowering systolic blood pressure? In this example, pd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the systolic blood pressure reading before the drug was taken minus the; reading after the drug was taken. What are the null and alternative hypotheses for the hypothesis test? H-0: mu_d notequalto 0 H_1: mu_d > 0 H_0: mu_d = 0 H_1: mu_d. 0 H_0: mu_d = 0 H_1: mu_dExplanation / Answer
Formulating the null and alternative hypotheses,
Ho: ud >= 0
Ha: ud < 0
At level of significance = 0.05
As we can see, this is a left tailed test.
The differences are:
-31
10
-9
-32
14
-5
-23
-62
-34
-19
-13
4
Calculating the standard deviation of the differences (third column):
s = 21.59264746
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 6.233260411
Calculating the mean of the differences (third column):
XD = -16.66666667
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = -2.673828072 [ANSWER, TEST STATISTIC]
**********************************************
As df = n - 1 = 11
Also, using p values, as this is left tailed,
p = 0.010822754 [ANSWER, P VALUE]
*******************************************
As P < 0.05, reject Ho. Hence,
1. LESS
2. REJECT
3. SUFFICIENT [ANSWERS]
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