The number of microwaves sold by an electronics shop each week can be modelled by a Poisson distribution with mean 5.
A random sample of 45 weeks is taken and the mean number of microwaves sold per week, Mˉ\bar{M}Mˉ, is calculated.
Write down the approximate distribution for the mean number of microwaves sold per week from a random sample of 45 weeks.
The number of coffee machines sold by the shop each week can be modelled by a Poisson distribution with mean μ\muμ.
A random sample of 60 weeks is taken and the mean number of coffee machines sold per week, Cˉ\bar{C}Cˉ, is found. The width of the 95% confidence interval for μ\muμ is 1.4.
Find an estimate for μ\muμ.
A second, independent random sample of 60 weeks is taken and a second 95% confidence interval for μ\muμ is found.
Find the probability that exactly one of these two confidence intervals contains μ\muμ.
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.