N2019 P2 Q9

A company produces resistors rated at \(750\) ohms for use in electronic circuits. The production manager wishes to test whether the mean resistance of these resistors is in fact \(750\) ohms. He knows that the resistances are normally distributed with variance \(100\text{ ohms}^2\).

1. Explain whether the manager should carry out a \(1\)-tail test or a \(2\)-tail test. State hypotheses for the test, defining any symbols you use.[2]

The production manager takes a random sample of \(8\) of these resistors. He finds that the resistances, in ohms, are as follows.

\[742\qquad771\qquad768\qquad738\qquad769\qquad752\qquad742\qquad766\]

2. Find the mean of the sample of \(8\) resistors. Carry out the test, at the \(5\%\) level of significance, for the production manager. Give your conclusion in context.[5]

The company also produces resistors rated at \(1250\) ohms. Nothing is known about the distribution of the resistances of these resistors.

3. Describe how, and why, a test of the mean resistance of the \(1250\) ohms resistors would need to differ from the test for the \(750\) ohms resistors.[2]