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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.