The discrete random variable X∼B(20,0.41)X \sim B(20, 0.41)X∼B(20,0.41)
Find P(3<X≤7)P(3 < X \leq 7)P(3<X≤7)
Previous research by a restaurant found that 30% of customers will order a starter.
On one day a random sample of 40 customers is taken and 7 order a starter.
Test at the 5% significance level whether the proportion of customers ordering a starter has decreased.
State the conclusion you would have reached if you tested at the 10% significance level.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.