Let X∼B(30,0.58)X\sim B(30,0.58)X∼B(30,0.58).
Find P(X≥12)P(X\geq12)P(X≥12). A cafe expects 30% of breakfast customers to order coffee. On one day, 19 of a random sample of 40 do so. For part (b), use H0:p=0.30H_0:p=0.30H0:p=0.30, H1:p>0.30 H_1:p>0.30\,H1:p>0.30 and Y∼B(40,0.30)Y\sim B(40,0.30)Y∼B(40,0.30) under H0H_0H0.
Explain why an upper-tail probability is required.
Calculate the exact p-value.
State the decision at the 1% level and give a conclusion in context.
State the conclusion at the 5% 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.