A precision engineering plant fills high-pressure gas cylinders to a volume, V V\,V mL, which follows a normal distribution N(μ,122)N(\mu, 12^2)N(μ,122). To monitor the consistency of the filling process, a random sample of n n\,n cylinders is selected and tested at the 1% level of significance using the following hypotheses:
H0:μ=1500andH1:μ<1500 H_0 : \mu = 1500 \quad \text{and} \quad H_1 : \mu < 1500 H0:μ=1500andH1:μ<1500Find, in terms of nnn, the critical region of the test.
The probability of a Type II error, when the true mean is μ=1490\mu = 1490μ=1490, is less than 0.05.
Find the minimum value of nnn.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.