In a study of the effect of a medical treatment, a simple random sample of 300 of the 500 participating patients was assigned to the treatment group; the remaining patients formed the control group.
When the patients were assessed at the end of the study, favorable outcomes were observed in 162 patients in the treatment group and 97 patients in the control group.
Did the treatment have an effect, or is this just chance variation? Perform a statistical test, following the steps in Problems 1 through 4.
Under the null hypothesis, the SE of the difference between the percents of favorable outcomes in the two groups is about _______%.
Have you followed the "steps in Problems 1 through 4"?
please tell me wat is SE, i Am not getting the right answer
To perform a statistical test to determine if the treatment had an effect, we can use hypothesis testing.
Step 1: Formulate the null hypothesis (H0) and alternative hypothesis (Ha):
H0: The treatment does not have an effect. The difference between the percentages of favorable outcomes in the treatment group and control group is due to chance.
Ha: The treatment does have an effect. The difference between the percentages of favorable outcomes in the treatment group and control group is not due to chance.
Step 2: Determine the level of significance (α). Let's assume we have a significance level of 5% (α = 0.05).
Step 3: Calculate the test statistic:
To compare the percentages of favorable outcomes in the treatment and control groups, we can calculate the standard error (SE) of the difference between the percentages. The formula for calculating SE is as follows:
SE = √ (p1(1-p1)/n1 + p2(1-p2)/n2)
Where:
- p1 is the proportion of favorable outcomes in the treatment group (162/300 = 0.54)
- p2 is the proportion of favorable outcomes in the control group (97/200 = 0.485)
- n1 is the sample size of the treatment group (300)
- n2 is the sample size of the control group (200)
Plugging in the values into the formula, we can calculate the SE.
SE = √ (0.54*(1-0.54)/300 + 0.485*(1-0.485)/200)
Step 4: Calculate the critical value and compare it with the test statistic:
To determine if the treatment has an effect, we need to calculate the critical value based on the significance level (α) and the degrees of freedom. Since we are comparing two proportions, the degrees of freedom will be (n1-1) + (n2-1) = 498.
Using the critical value or p-value, we can make a decision. If the test statistic falls into the rejection region (beyond the critical value), we reject the null hypothesis. If it falls within the acceptance region (inside the critical value), we fail to reject the null hypothesis.
To answer the question, the SE of the difference between the percentages of favorable outcomes in the two groups can be calculated using the formula mentioned earlier. The specific value would depend on inputting the given values into the formula.