experimental Placebo
(n=100) (n=100)
Mean BP 120.2(15.4) (131.4(18.9)
Hypertentive(%) 14 22
side effect (%) 6 8
Trial involve 200 subject,rendomally receiving either medication or placebo. The data collected at the end of trialafter 6 week study.
a) test if there is significance difference in mean systolic blood pressure between group using alpha=0.05
b)test if there is a significant difference in the porporation of hypertensive patients between groups using alpha=0.05.
To answer these questions, we will perform a hypothesis test using the appropriate statistical method. Let's start with question (a) and test the significance difference in mean systolic blood pressure between the experimental group and the placebo group using an alpha level of 0.05.
Step 1: State the null hypothesis (H0) and alternative hypothesis (Ha):
- Null hypothesis (H0): There is no significant difference in mean systolic blood pressure between the experimental group and the placebo group.
- Alternative hypothesis (Ha): There is a significant difference in mean systolic blood pressure between the experimental group and the placebo group.
Step 2: Select an appropriate statistical test:
Since we are comparing the means of two independent groups, we can use the independent samples t-test. The t-test will allow us to determine if there is a statistically significant difference in the means.
Step 3: Calculate the test statistic:
Calculate the t-value by using the formula:
t = (mean1 - mean2) / √[(s1^2/n1) + (s2^2/n2)]
where:
mean1 and mean2 are the means of the two groups,
s1 and s2 are the standard deviations of the two groups,
n1 and n2 are the sample sizes of the two groups.
In our case, from the given data:
mean1 (experimental group) = 120.2
mean2 (placebo group) = 131.4
s1 (experimental group standard deviation) = 15.4
s2 (placebo group standard deviation) = 18.9
n1 (experimental group sample size) = 100
n2 (placebo group sample size) = 100
Using these values, we can calculate the t-value.
Step 4: Determine the critical value or p-value:
For an alpha level of 0.05, we need to determine the critical value or p-value to determine whether to reject the null hypothesis.
Step 5: Compare the test statistic with the critical value or p-value:
If the calculated t-value is greater than the critical value or if the p-value is less than the alpha level (0.05), we reject the null hypothesis and conclude that there is a significant difference in mean systolic blood pressure between the two groups. Otherwise, we fail to reject the null hypothesis.
Let me calculate the t-value and compare it with the critical value or p-value.