The weights of a random sample of 12 luxury chocolates are measured. The mean weight of the sample is recorded as 42.5 g42.5\text{ g}42.5 g. The weights of the chocolates are known to be normally distributed.
Given that the population standard deviation is 0.8 g0.8\text{ g}0.8 g,
estimate the limits between which 95%95\%95% of the weights of individual chocolates lie.
find a 99%99\%99% confidence interval for the mean weight of the chocolates.
A quality control manager claims that the mean weight of these chocolates is 41.8 g41.8\text{ g}41.8 g.
Comment on the manager's claim. Give a reason for your answer.
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.