OCR Further Statistics 2023 June — Question 5

Exam BoardOCR
ModuleFurther Statistics (Further Statistics)
Year2023
SessionJune
TopicWilcoxon tests

5 An historian has reason to believe that the average age at which men got married in the seventeenth century was higher in urban areas compared to rural areas. The historian collected data from a random sample of 8 men in an urban area and a random sample of 6 men in a rural area, all of whom were married in the seventeenth century. The results were as follows, given in the form years/months.
Urban:\(18 / 3\)\(18 / 5\)\(19 / 9\)\(20 / 7\)\(25 / 6\)\(34 / 6\)\(41 / 8\)\(46 / 3\)
Rural:\(18 / 0\)\(18 / 1\)\(18 / 4\)\(19 / 11\)\(22 / 2\)\(28 / 11\)
  1. Use an appropriate non-parametric method to test at the \(5 \%\) significance level whether the average age at marriage of men is higher in urban areas than in rural areas.
  2. When checking the data, the historian found that the age of one of the men, Mr X, which had been recorded as 28/11, had been wrongly recorded. When corrected, the result of the test in part (a) was unchanged. Determine the youngest age that Mr X could have been, given that it was not the same, in years and months, as that of any of the other men in the sample.