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.