606 STATISTICS AND PROBABILITY
a level of significance of 0.01.(Bessel’s correction isσˆ^2 =s^2 N
N− 1). ⎡ ⎢ ⎢ ⎢ ⎣x 1 = 23 .7,s 1 = 1 .73,
σ 1 = 1 .93,x 2 = 25 .7,
s 2 = 2 .50,σ 2 = 2 .80,
|t|= 1 .62,t 0. 995 ν 8 = 3 .36,
hence hypothesis is accepted⎤⎥
⎥
⎥
⎦- A sample of 100 relays produced by manufac-
turerAoperated on average 1190 times before
failure occurred, with a standard deviation of
90.75. Relays produced by manufacturerB,
operated on average 1220 times before failure
with a standard deviation of 120. Determine
if the number of operations before failure are
significantly different for the two manufac-
turers at a level of significance of (a) 0.05
and (b) 0.1.
⎡
⎢
⎢
⎢
⎣z(sample)= 1 .99,
(a)z 0. 05 , two-tailed test=± 1 .96,
no significance,(b)z 0. 1 , two-tailed test=± 1 .645,
significant difference⎤⎥
⎥
⎥
⎦- A sample of 12 car engines produced
by manufacturerAshowed that the mean
petrol consumption over a measured dis-
tance was 4.8 litres with a standard devia-
tion of 0.40 litres. Twelve similar engines
for manufacturer B were tested over the
same distance and the mean petrol consump-
tion was 5.1 litres with a standard deviation
of 0.36 litres. Test the hypothesis that the
engines produced by manufacturer A are
more economical than those produced by
manufacturerBat a level of significance of
(a) 0.01 and (b) 0.1.
⎡ ⎢ ⎢ ⎢ ⎢ ⎣
Assuming null hypothesis of no
difference,σ= 0 .397,|t|= 1 .85,
(a)t 0. 995 ,ν 22 = 2 .82, hypothesis
rejected,
(b)t 0. 95 ,ν 22 = 1 .72, hypothesis
accepted⎤ ⎥ ⎥ ⎥ ⎥ ⎦- Four-star and unleaded petrol is tested in
5 similar cars under identical conditions. For
four-star petrol, the cars covered a mean
distance of 21.4 kilometres with a standard
deviation of 0.54 kilometres for a given
mass of petrol. For the same mass of
unleaded petrol, the mean distance covered
was 22.6 kilometres with a standard devia-
tion of 0.48 kilometres. Test the hypothesis
that unleaded petrol gives more kilometres
per litre than four-star petrol at a level of
significance of 0.1.
[
σ= 0 .571,|t|= 3 .32,t 0. 95 ,
ν 8 = 1 .86, hence hypothesis
is rejected
]