Hypothesis tests for a binomial proportionEdexcel A-Level Maths: Mind map

Exam questions on Hypothesis tests for a binomial proportion

1. A drug is known to cure 30% of patients with a certain condition. A new drug is tested on 20 randomly chosen patients, of whom 10 are cured. Let $p$ be the probability that a patient given the new drug is cured and let $X$ be the number cured in a sample of 20. The company tests at the 5% significance level whether the new drug is more effective.
   State the conclusion of the test, in context.2 marks
2. A company claims that 85% of its parcels are delivered on time. A customer believes that the proportion is lower. In a random sample of 15 parcels, 10 are delivered on time. Let $p$ be the proportion of all the company's parcels that are delivered on time and let $X$ be the number delivered on time in a sample of 15. The customer tests at the 5% significance level.
   State the conclusion of the test, in context.2 marks
3. A network provider claims that 40% of its customers are on a premium plan. A researcher believes that the proportion has changed. In a random sample of 30 customers, 17 are on a premium plan. Let $X$ be the number of customers on a premium plan in a sample of 30.
   State the hypotheses for a test at the 5% significance level, and say what $p$ represents.3 marks