OCR MEI S4 2009 June — Question 3

Exam BoardOCR MEI
ModuleS4 (Statistics 4)
Year2009
SessionJune
TopicHypothesis test of a normal distribution
3
  1. At a waste disposal station, two methods for incinerating some of the rubbish are being compared. Of interest is the amount of particulates in the exhaust, which can be measured over the working day in a convenient unit of concentration. It is assumed that the underlying distributions of concentrations of particulates are Normal. It is also assumed that the underlying variances are equal. During a period of several months, measurements are made for method A on a random sample of 10 working days and for method B on a separate random sample of 7 working days, with results, in the convenient unit, as follows.
    Method A124.8136.4116.6129.1140.7120.2124.6127.5111.8130.3
    Method B130.4136.2119.8150.6143.5126.1130.7
    Use a \(t\) test at the \(10 \%\) level of significance to examine whether either method is better in resulting, on the whole, in a lower concentration of particulates. State the null and alternative hypotheses under test.
  2. The company's statistician criticises the design of the trial in part (i) on the grounds that it is not paired. Summarise the arguments the statistician will have used. A new trial is set up with a paired design, measuring the concentrations of particulates on a random sample of 9 paired occasions. The results are as follows.
    PairIIIIIIIVVVIVIIVIIIIX
    Method A119.6127.6141.3139.5141.3124.1116.6136.2128.8
    Method B112.2128.8130.2134.0135.1120.4116.9134.4125.2
    Use a \(t\) test at the \(5 \%\) level of significance to examine the same hypotheses as in part (i). State the underlying distributional assumption that is needed in this case.
  3. State the names of procedures that could be used in the situations of parts (i) and (ii) if the underlying distributional assumptions could not be made. What hypotheses would be under test?
This paper (4 questions)
View full paper
Q1 Q2 Q3 Q4