RI/2021/JC2/Prelim/P2/Q06

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.

[2]

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.

[5]

(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.

[1]