OCR MEI S2 2012 June — Question 4 9 marks

Exam BoardOCR MEI
ModuleS2 (Statistics 2)
Year2012
SessionJune
Marks9
TopicChi-squared distribution
4
  1. Mary is opening a cake shop. As part of her market research, she carries out a survey into which type of cake people like best. She offers people 4 types of cake to taste: chocolate, carrot, lemon and ginger. She selects a random sample of 150 people and she classifies the people as children and adults. The results are as follows.
    \multirow{2}{*}{}Classification of person\multirow{2}{*}{Row totals}
    ChildAdult
    \multirow{4}{*}{Type of cake}Chocolate342357
    Carrot161834
    Lemon41822
    Ginger132437
    Column totals6783150
    The contributions to the test statistic for the usual \(\chi ^ { 2 }\) test are shown in the table below.
    Classification of person
    \cline { 3 - 4 } \multicolumn{2}{|c|}{}ChildAdult
    \multirow{3}{*}{
    Type
    of
    cake
    }    		Chocolate2.86462.3124
    \cline { 2 - 4 }Carrot0.04360.0352
    \cline { 2 - 4 }Lemon3.45492.7889
    \cline { 2 - 4 }Ginger0.75260.6075
    The sum of these contributions, correct to 2 decimal places, is 12.86 .
    1. Calculate the expected frequency for children preferring chocolate cake. Verify the corresponding contribution, 2.8646, to the test statistic.
    2. Carry out the test at the \(1 \%\) level of significance.
  2. Mary buys flour in bags which are labelled as containing 5 kg . She suspects that the average contents of these bags may be less than 5 kg . In order to test this, she selects a random sample of 8 bags and weighs their contents. Assuming that weights are Normally distributed with standard deviation 0.0072 kg , carry out a test at the \(5 \%\) level, given that the weights of the 8 bags in kg are as follows.
    4.992
    4.981
    4.982
    4.996
    4.991
    5.006
    5.009
    5.003
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