- (a) State two reasons why stratified sampling might be chosen as a method of sampling when carrying out a statistical survey.
(b) State one advantage and one disadvantage of quota sampling. - A sample of size 5 is taken from a population that is normally distributed with mean 10 and standard deviation 3 . Find the probability that the sample mean lies between 7 and 10 .
(Total 6 marks) - A researcher carried out a survey of three treatments for a fruit tree disease. The contingency table below shows the results of a survey of a random sample of 60 diseased trees.
| No action | Remove diseased branches | Spray with chemicals |
| Tree died within 1 year | 10 | 5 | 6 |
| Tree survived for 1-4 years | 5 | 9 | 7 |
| Tree survived beyond 4 years | 5 | 6 | 7 |
Test, at the \(5 \%\) level of significance, whether or not there is any association between the treatment of the trees and their survival. State your hypotheses and conclusion clearly.
(Total 11 marks)