The discrete random variable X X\,X has the distribution X∼B(20,0.41)X \sim B(20, 0.41)X∼B(20,0.41).
Find P(3<X≤7)P(3 < X \le 7)P(3<X≤7).
A transport survey records that 30% of commuters usually travel by bus. After a route change, a random sample of 50 commuters is taken, and 9 of them usually travel by bus. Stating your hypotheses clearly, test at the 5% significance level whether the proportion of commuters travelling by bus has decreased.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.