A new drug will not be considered for acceptance by Health Canada unless it causes serious side effects in less than 0.01percent of the population

Question

A new drug will not be considered for acceptance by Health Canada unless it causes serious side
effects in less than 0.01percent of the population. In a trial with 80,000 people, 9 suffered serious side effects.
Test the significance of this result with alpha = 0.01. Do you recommend that this drug be accepted?
Explain why or why not

Answer 1

Hi Ali,

You check whether or not the drug would be accepted by conducting a hypothesis testing. There are five steps in any hypothesis testing procedure. Let’s see them one by one.

Step 1: Develop H0 and Ha

We start with the assumption that the drug will be accepted. That is, it causes serious side
effects in less than 0.01percent of the population. This is mathematically stated as p<0.0001. Since this statement specifies direction, you take it as an alternative hypothesis. Therefore, Ha: p<0.0001.

Once you determine Ha as such, you then specify H0. H0 and Ha are competing statements that vie for acceptance. In addition, Ha and Ha are mutually exclusive and collectively exhaustive. The statement that meets both of these requirements is H0: p>0.0001

Thus, H0 and Ha can be stated as:
H0: p>0.0001
Ha: p<0.0001.

Step 2: Determine the test statistic to be used

We use a z-test to test the hypothesis, and we have a left-tailed test

 

Step 3: Specify the level of significance, α, determine the critical value and state the decision rule

Alpha = 0.01

The critical value (Z table value) corresponding to alpha = 0.01 is 2.33. Since we have a left-tailed test, it becomes -2.33. Thus, we state the decision rule as
Reject H0 if sample statistic < -2.33

Step 4: Collect sample data and compute the sample statistic

From the data given, n=80,000; the number of people who experienced side effects (x) = 9. So, the proportion of patients who experienced serious side effects, p-bar = 0.0001125.

Then we compute the sample statistic using the following formula:
Where q = 1-P
Z= (0.0001125-0.0001)/√((0.0001*0.9999)/80,000)
Z = +0.35
Step 5: Make the decision
We compare the critical value (-2.33) with the sample statistic (+0.35) and make the decision. Since 0.35 > -2.33, we do not reject the null hypothesis.

Since we are not rejecting H0, we reject Ha. That means, the drug should not be accepted.

I hope it helps