A pharmaceutical company produces tablets. The mass, X X\,X mg, of the tablets follows a normal distribution N(μ,32)N(\mu, 3^2)N(μ,32). To monitor the production process, a random sample of n n\,n tablets is selected and tested at the 5% level of significance using the following hypotheses:
H0:μ=250andH1:μ>250 H_0 : \mu = 250 \quad \text{and} \quad H_1 : \mu > 250 H0:μ=250andH1:μ>250Find, in terms of nnn, the critical region of the test.
The probability of a Type II error, when the true mean is μ=252\mu = 252μ=252, is less than 0.10.
Find the minimum value of nnn.
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.