1 A meteorologist claims that the median daily rainfall in London is 2.2 mm . A single sample sign test is to be used to test the claim, using the following hypotheses:
\(\mathrm { H } _ { 0 }\) : a sample comes from a population with median 2.2,
\(\mathrm { H } _ { 1 }\) : the sample does not come from a population with median 2.2.
30 randomly selected observations of daily rainfall in London are compared with 2.2, and given a '+' sign if greater than 2.2 and a '-' sign if less than 2.2. (You may assume that no data values are exactly equal to 2.2.) The test is to be carried out at the \(5 \%\) level of significance. Let the number of ' + ' signs be \(k\). Find, in terms of \(k\), the critical region for the test showing the values of any relevant probabilities.