The discrete random variable X X\,X has the distribution X∼B(30,0.58)X \sim B(30, 0.58)X∼B(30,0.58).
Find P(X≥12)P(X \ge 12)P(X≥12).
A cafe expects 30% of its customers to order a coffee with breakfast. On one day a random sample of 40 customers who ordered breakfast is taken, and 19 of them order a coffee. Stating your hypotheses clearly, test at the 1% significance level whether the proportion of customers ordering a coffee has increased.
State the conclusion you would have reached if a 5% significance level had been used.
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.