A textile manufacturer produces fabric where flaws occur randomly at a constant rate of 1 flaw every 15 metres. After a maintenance check of the looms, a random sample of 60 metres of fabric is inspected to see if the rate of flaws has changed.
Stating your hypotheses clearly and using a 10% level of significance, find the critical region for this test. You should choose your critical region so that the probability of rejection is less than 0.05 in each tail.
State the actual significance level of this test.
A consultant suggests a new weaving adjustment that they claim will reduce the rate of flaws. The manufacturer tests this by inspecting a random sample of 300 metres of fabric produced with the adjustment and finds 13 flaws.
Using a suitable approximation, test the consultant's claim at a 5% level of significance. State your hypotheses clearly.
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.