Assume a simple random sample has been taken, the conditions for binomial distribution are met and the sample proportions can be approximated by a normal distribution. In order to evaluate a course of therapy to treat brain tumors, a sample of 300 patients revealed that 96 patients were responsive to a certain course of treatment. Test the claim that more than 30% of patients with brain tumors were responsive to the treatment. Use a 0.01 significance level.What is the alternative hypothesis?
To determine the alternative hypothesis, we first need to state the null hypothesis. In this case, the null hypothesis (H0) is that the proportion of patients with brain tumors who are responsive to the treatment is equal to 30% (0.30).
Now, for the alternative hypothesis (Ha), we need to consider the claim being tested. The claim is that more than 30% of patients with brain tumors are responsive to the treatment. Therefore, the alternative hypothesis should reflect this claim.
In mathematical terms, the alternative hypothesis can be written as follows:
Ha: p > 0.30
where p represents the population proportion of patients with brain tumors who are responsive to the treatment.
So, the alternative hypothesis is that the proportion of responsive patients (p) is greater than 0.30.