3 The wing lengths of native English male blackbirds, measured in mm , are Normally distributed with mean 130.5 and variance 11.84.
- Find the probability that a randomly selected native English male blackbird has a wing length greater than 135 mm .
- Given that \(1 \%\) of native English male blackbirds have wing length more than \(k \mathrm {~mm}\), find the value of \(k\).
- Find the probability that a randomly selected native English male blackbird has a wing length which is 131 mm correct to the nearest millimetre.
It is suspected that Scandinavian male blackbirds have, on average, longer wings than native English male blackbirds. A random sample of 20 Scandinavian male blackbirds has mean wing length 132.4 mm . You may assume that wing lengths in this population are Normally distributed with variance \(11.84 \mathrm {~mm} ^ { 2 }\).
- Carry out an appropriate hypothesis test, at the \(5 \%\) significance level.
- Discuss briefly one advantage and one disadvantage of using a \(10 \%\) significance level rather than a \(5 \%\) significance level in hypothesis testing in general.