there are 200 subjects enrolled to receive either experimental medications or placebo. At the end of study following data is collected after 6 week.
(sd)= standard deviation.
BP= blood pressure.
experimental meds placebo
(n=100) (n=100)
Mean BP 120.2(sd 15.4) 131.4(sd18.9)
High BP 14% 22%
Side effect 6% 8%
a)Test if there is a significant difference in mean BP between two groups using alpha=0.05.
b) Test if there is a significant difference in the proportion of high BP patients between groups using alpha=0.05.
To test if there is a significant difference in mean blood pressure (BP) between the two groups, we can use a two-sample t-test.
a) Here are the steps to perform the two-sample t-test:
Step 1: State the hypotheses.
The null hypothesis (H0) states that there is no significant difference in mean BP between the experimental medication and placebo groups. The alternative hypothesis (Ha) states that there is a significant difference in mean BP between the two groups.
H0: μ1 = μ2 (there is no difference in mean BP)
Ha: μ1 ≠ μ2 (there is a difference in mean BP)
Step 2: Calculate the test statistic.
We can use the formula for the two-sample t-test:
t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
From the given data:
x1 = 120.2
x2 = 131.4
s1 = 15.4
s2 = 18.9
n1 = n2 = 100
Substituting these values into the formula, we can calculate the test statistic.
Step 3: Determine the critical value.
Since the significance level (alpha) is given as 0.05, we need to find the critical value for a two-tailed test at a 95% confidence level.
Step 4: Compare the test statistic with the critical value.
If the absolute value of the calculated test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a significant difference in mean BP between the two groups. Otherwise, we fail to reject the null hypothesis.
Step 5: State the conclusion.
Based on the comparison, we will state whether there is a significant difference in mean BP between the two groups or not.
Now let's move on to part b.
To test if there is a significant difference in the proportion of high BP patients between the experimental medication and placebo groups, we can use a two-sample z-test for proportions.
b) Here are the steps to perform the two-sample z-test for proportions:
Step 1: State the hypotheses.
The null hypothesis (H0) states that there is no significant difference in the proportion of high BP patients between the two groups. The alternative hypothesis (Ha) states that there is a significant difference in the proportion of high BP patients.
H0: p1 = p2 (there is no difference in the proportions)
Ha: p1 ≠ p2 (there is a difference in the proportions)
Step 2: Calculate the test statistic.
We can use the formula for the two-sample z-test for proportions:
z = (p1 - p2) / sqrt((p * (1 - p) / n1) + (p * (1 - p) / n2))
where p1 and p2 are the sample proportions, p is the overall sample proportion, and n1 and n2 are the sample sizes.
From the given data:
p1 = 0.14 (14% converted to proportion)
p2 = 0.22 (22% converted to proportion)
n1 = n2 = 100
Substituting these values into the formula, we can calculate the test statistic.
Step 3: Determine the critical value.
Since the significance level (alpha) is given as 0.05, we need to find the critical value for a two-tailed test at a 95% confidence level.
Step 4: Compare the test statistic with the critical value.
If the absolute value of the calculated test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a significant difference in the proportion of high BP patients between the two groups. Otherwise, we fail to reject the null hypothesis.
Step 5: State the conclusion.
Based on the comparison, we will state whether there is a significant difference in the proportion of high BP patients between the two groups or not.