A company tests H0:p=0.7H_0:p=0.7H0:p=0.7 against H1:p<0.7 H_1:p<0.7\,H1:p<0.7 using a random sample of 45 outcomes. Its critical region is X≤24X\leq24X≤24.
Calculate the actual significance level.
Describe a Type I error in this context, where success means an order arrives on time.
Explain how increasing the sample size can improve the test while keeping the significance level no greater than 2.5%.
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.