A hypothesis test at the 1% significance level leads to the rejection of H0H_0H0. Explain why this does not prove that H1 H_1\,H1 is true.
Explain why raising the significance level from 1% to 5% makes it easier to reject H0H_0H0.
For a two-tailed test on a binomial proportion at a nominal 5% significance level, the critical region chosen has an actual significance level of 4.31%. Explain why the two figures differ, and state the consequence for the test.
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.