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 test the claim that more than 30% of patients with brain tumors are responsive to the treatment, we need to state our null and alternative hypotheses.

Null Hypothesis (H₀): The proportion of patients with brain tumors who are responsive to the treatment is 30% or less. In mathematical notation, H₀: p ≤ 0.30.

Alternative Hypothesis (H₁): The proportion of patients with brain tumors who are responsive to the treatment is more than 30%. In mathematical notation, H₁: p > 0.30.

Therefore, the alternative hypothesis is that the proportion is greater than 30%.