- A factory produces bolts. The lengths of the bolts are normally distributed with mean \(\mu \mathrm { mm }\) and standard deviation 0.868 mm
A random sample of 15 of these bolts is taken and the mean length is 30.03 mm
- Calculate a 90\% confidence interval for \(\mu\)
A suitable test, at the \(10 \%\) level of significance, is carried out using these 15 bolts, to see whether or not there is evidence that the variance of the length of the bolts has increased.
- Calculate the critical region for \(S ^ { 2 }\)
The manager of the factory decides that, in future, he will check each month whether the machine making the bolts is working properly. He uses a \(10 \%\) level of significance to test whether or not there is evidence that
- the mean length of the bolts has changed
- the variance of the length of the bolts has increased
The next month a random sample of 15 bolts is taken.
The mean length of these bolts is 30.06 mm and the standard deviation is 1.02 mm - With reference to your answers to part (a) and part (b), state whether or not there is any evidence that the machine is not working properly.
Give reasons for your answer.