The volume of orange juice in a carton produced by a bottling machine is normally distributed with a mean of 252 ml and a standard deviation of 3.5 ml.
Find the probability that a randomly selected carton of orange juice contains less than 245 ml.
Write down the null and alternative hypotheses to test if the mean volume is lower than 252 ml.
A sample of 30 cartons is taken and the mean volume is found to be 251 ml. Carry out a test at the 5% significance level to see if there is evidence that the machine is producing cartons with a mean of less than 252 ml.
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.