Give two reasons why an investigator might need to take a sample in order to obtain information about a population.
State two requirements of a sample.
Discuss briefly the advantage of the sampling being random.
Under what circumstances might one use a Wilcoxon single sample test in order to test a hypothesis about the median of a population? What distributional assumption is needed for the test?
On a stretch of road leading out of the centre of a town, highways officials have been monitoring the speed of the traffic in case it has increased. Previously it was known that the median speed on this stretch was 28.7 miles per hour. For a random sample of 12 vehicles on the stretch, the following speeds were recorded.
$$\begin{array} { l l l l l l l l l l l l }
32.0 & 29.1 & 26.1 & 35.2 & 34.4 & 28.6 & 32.3 & 28.5 & 27.0 & 33.3 & 28.2 & 31.9
\end{array}$$
Carry out a test, with a \(5 \%\) significance level, to see whether the speed of the traffic on this stretch of road seems to have increased on the whole. [0pt]
[10]