In: Statistics and Probability
Experimental (n=100) |
Placebo (n=100) |
|
Mean (SD) Systolic Blood Pressure |
120.2 (15.4) |
131.4 (18.9) |
% Hypertensive |
14% |
22% |
% With Side Effects |
6% |
8% |
Is there a significant difference in the proportions of hypertensive patients between groups? Use α = 0.05.
Step 1. Set up hypotheses and determine level of significance
Step 2. Select the appropriate test statistic
Step 3. Set up decision rule
Step 4. Compute the test statistic
step 5. conclusion
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1 = P2
Alternative hypothesis: P1 P2
Note that these hypotheses constitute a two-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 *
n2) / (n1 + n2)
p = 0.18
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2)
] }
SE = 0.05433
z = (p1 - p2) / SE
z = - 1.47
zcritical = + 1.96
Rejection region is - 1.96 > z > 1.96
Reject H0, - 1.96 > z > 1.96
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a two-tailed test, the P-value is the probability that the z-score is less than -1.47 or greater than 1.47.
Thus, the P-value = 0.142
Interpret results. Since the P-value (0.142) is greater than the significance level (0.05), we cannot accept the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that there a significant difference in the proportions of hypertensive patients between groups.