# s2 jan 2012 helpWatch

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#1
some tricky questions..

It is desired to test whether the average amount of sleep obtained by school pupils in Year 11 is 8 hours,
based on a random sample of size 64. The population standard deviation is 0.87 hours and the sample mean
is denoted by H¯. The critical values for the test are H¯ = 7.72 and H¯ = 8.28.
Calculate the significance level of the test.

also another q i haven't seen the format of before:
Six prizes are allocated, using random numbers, to a group of 12 girls and 8 boys. Calculate the
probability that exactly 4 of the prizes are allocated to girls if
(a) the same child may win more than one prize, [2]
(b) no child may win more than one prize. [2]
(ii) Sixty prizes are allocated, using random numbers, to a group of 1200 girls and 800 boys. Use a suitable approximation to calculate the probability that at least 30 of the prizes are allocated to girls. Does it affect your calculation whether or not the same child may win more than one prize?
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