A manufacturer knows that 12% of its light bulbs fail within a year. A new production method is introduced, and the manufacturer wants to know whether the proportion failing within a year has changed.
A random sample of 200 bulbs made by the new method is taken, and X X\,X is the number that fail within a year.
State suitable null and alternative hypotheses for the manufacturer's test.
State the distribution of X X\,X under the null hypothesis.
State whether this test is one-tailed or two-tailed.
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.