A company produces steel rods whose lengths follow a normal distribution with mean μ\muμ cm and standard deviation σ\sigmaσ cm. A random sample of 16 rods is measured. From this sample, the unbiased estimate of the mean is xˉ=122.4\bar{x} = 122.4xˉ=122.4 and the unbiased estimate of the variance is s2=3.84s^2 = 3.84s2=3.84.
Test, at the 5% level of significance, whether or not σ\sigmaσ is greater than 1.5. State your hypotheses clearly.
Test, at the 5% level of significance, whether or not μ\muμ is greater than 121.5.
State an assumption about the distribution of rod lengths that is necessary for these tests to be valid.
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.