The recruitment manager of the private car hire company, I-ber, claims that the mean weckly earnings of a full-time driver is \(\$ 980\). The managing director suspects that the mean weekly earmings is less than \(\$ 980\) and he instructs the recruitment manager to carry out a hypothesis test on a sample of drivers. It is given that the population standard deviation of the weckly earnings is \(\$ 88\).

(i) State suitable hypotheses for the test, defining any symbols that you use.


The recruitment manager takes a random sample of 10 drivers. He finds that the weekly carnings in dollars, are as follows.

$\begin{array}{llllllllll}942 & 950 & 905 & 1003 & 883 & 987 & 924 & 920 & 913 & 968\end{array}$

(ii) Find the mean weekly earnings of the sample of these 10 drivers. Carry out the test, at (5 %) Ievel of significance, for the recruitment manager. Give your conclusion in context and state a necessary assumption for the test to be valid.


(iii) Find the smallest level of significance at which the test would result in rejection of the null hypothesis, giving your answer correct to 1 decimal place.