Question 5 (20 Marks)
(a) Two different machines A and B are used to fill packets of sweets. The owner of
the company decides to assess the performance of the two machines. He selects a
sample of 50 packets filled by machine A and a sample of 60 packets filled by
machine B. The masses of sweets, x kg, in packets filled by machine A and the
masses of sweets, y kg, in packets filled by machine B are summarised as follows:
$\sum x = 22.4$ $\sum x^2 = 10.1$ $\sum y = 28.8$ $\sum y^2 = 16.3$
A hypothesis test at the $\alpha$% level of significance provides evidence that the mean
mass of sweets in packets filled by machine A is less than the mean mass of sweets
in packets filled by machine B. Find the set of possible values of $\alpha$.
[10 marks]
(b) The time taken, in seconds, for a random sample of 9 athletes to run 400m, before
and after a training scheme are tabulated as follows:
Athlete
A
B
C
D
E
F
G
H
I
Time before 48.8 48.2 50.3 49.6 49.4 48.9 47.6 50.3 48.4
Time after 47.9 47.8 49.6 49.1 49.6 48.9 47.7 49.1 48.1
The organiser of the training scheme claims that on average an athlete's time will
be reduced by at least 0.3 seconds.
Test at the 10% significance level whether the organiser's claim is justified, stating
any assumption.
[10 marks]
