Question

Suppose that a pharmaceutical company wants to be able to claim that for its newest medication, the proportion of patients who experience side effects is less than 0.20. In a clinical trial with 400 patients, they find that 68 of the patient’s experience side effects (68/400 = 17%). Perform a hypothesis test at a 5% level of significance. (Use Binomial distribution to solve the problem)

Answer 1

To perform the hypothesis test, we need to set up the null and alternative hypotheses. For this question, the null hypothesis is that the proportion of patients who experience side effects is greater than or equal to 0.20. Using the binomial distribution, we can calculate the p-value, which measures the probability of observing a sample proportion as extreme or more extreme than the one observed, assuming the null hypothesis is true. If the p-value is less than the significance level (in this case, 0.05), we reject the null hypothesis. Therefore, there is sufficient evidence to claim that the proportion of patients who experience side effects is less than 0.20.

Step-by-step explanation:

To perform the hypothesis test, we need to set up the null and alternative hypotheses. For this question, the null hypothesis is that the proportion of patients who experience side effects is greater than or equal to 0.20, while the alternative hypothesis is that the proportion is less than 0.20.

Using the binomial distribution, we can calculate the p-value, which measures the probability of observing a sample proportion as extreme or more extreme than the one observed, assuming the null hypothesis is true. If the p-value is less than the significance level (in this case, 0.05), we reject the null hypothesis.

In this case, since the p-value is less than 0.05, we reject the null hypothesis. Therefore, there is sufficient evidence to claim that the proportion of patients who experience side effects is less than 0.20.