Question

Two popular drugs used for the treatment of depression are Resithan and Exemor. A random sample of 541 depressed individuals is selected and treated with Resithan, and 251 find relief from their depression. A random sample of 528 depressed individuals is independently selected from the first sample and treated with Exemor, and 213 find relief from their depression. Can we conclude, at the 0.05 level of significance, that the proportion of all depressed individuals taking Resithan who find relief from depression is greater than the proportion of all depressed individuals taking Exemor who find relief from depression?

Answer 1

To test if the proportion finding relief from depression is greater with Resithan compared to Exemor, a hypothesis test for two proportions is performed. Our null hypothesis states that there is no difference or Exemor is better, while the alternative suggests that Resithan is better. The test statistic is compared to a critical value to determine if we can reject the null hypothesis.

Step-by-step explanation:

To determine if there is a significant difference between the proportions of individuals finding relief from depression after taking Resithan compared to those taking Exemor, a hypothesis test for two proportions is conducted at the 0.05 level of significance. The steps are as follows:

1. Define the null hypothesis (H0) as the proportion of individuals finding relief with Resithan (p1) being equal to or less than the proportion finding relief with Exemor (p2), i.e., H0: p1 ≤ p2.
2. Define the alternative hypothesis (Ha) as the proportion of individuals finding relief with Resithan being greater than with Exemor, i.e., Ha: p1 > p2.
3. Calculate the sample proportions: p1 = 251/541 for Resithan, p2 = 213/528 for Exemor.
4. Calculate the pooled sample proportion, which is (251 + 213) / (541 + 528).
5. Calculate the standard error of the difference between the two proportions.
6. Calculate the test statistic (z) using the sample proportions, the pooled sample proportion, and the standard error.
7. Compare the test statistic to the critical value from the standard normal distribution for a one-tailed test at the 0.05 level of significance: If z is greater than the critical value, reject the null hypothesis.
8. Interpret the results: If the null hypothesis is rejected, it suggests that there is enough evidence to conclude that the proportion of individuals finding relief from depression is greater with Resithan than with Exemor.