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In summer the growth rate of grass in a lawn has a normal distribution with mean 3.2 cm per week and
standard deviation 1.4 cm per week. A new type of grass is introduced which the manufacturer claims
has a slower growth rate. A hypothesis test of this claim at the 5% significance level was carried out
using a random sample of 10 lawns that had the new grass. It may be assumed that the growth rate of
the new grass has a normal distribution with standard deviation 1.4 cm per week.
(i) Find the rejection region for the test. [4]
(ii) The probability of making a Type II error when the actual value of the mean growth rate of
the new grass is m cm per week is less than 0.5. Use your answer to part (i) to write down an
inequality for m.