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 _______%.
To determine whether the treatment had an effect or if the observed outcomes were due to chance, we can perform a statistical test. The steps to follow are as follows:
1. Define the null and alternative hypothesis:
- Null hypothesis (H0): The treatment has no effect, and the difference in the percentages of favorable outcomes between the treatment and control groups is due to chance.
- Alternative hypothesis (HA): The treatment has an effect, and the difference in the percentages of favorable outcomes between the treatment and control groups is not due to chance.
2. Calculate the observed difference in percentages of favorable outcomes:
- In the treatment group, 162 out of 300 patients had favorable outcomes, which is 54% (162/300 * 100).
- In the control group, 97 out of 200 patients had favorable outcomes, which is 48.5% (97/200 * 100).
- The observed difference in percentages of favorable outcomes is 54% - 48.5% = 5.5%.
3. Calculate the standard error (SE) of the difference between the percentages of favorable outcomes:
- The standard error can be calculated using the formula:
SE = sqrt(p1 * (1 - p1) / n1 + p2 * (1 - p2) / n2),
where p1 and p2 are the percentages of favorable outcomes, and n1 and n2 are the sample sizes for the treatment and control groups, respectively.
- In this case, p1 = 54%, n1 = 300, p2 = 48.5%, and n2 = 200.
- Calculate SE using the given values.
4. Calculate the SE as a percentage:
- Once you obtain the SE value, you can convert it into a percentage by multiplying it by 100.
- Calculate the SE as a percentage for the obtained SE value.
Following these steps, you should be able to calculate the SE of the difference between the percentages of favorable outcomes in the treatment and control groups under the null hypothesis.