Calculate expected frequencies

A question is this type if and only if it requires calculating expected frequencies for a chi-squared test from probabilities or from marginal totals in a contingency table.

2 questions · Moderate -0.6

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Edexcel S3 2023 January Q3
9 marks Moderate -0.8
3 A mobile phone company offers an insurance policy to its customers when they purchase a mobile phone. The company conducted a survey on the age of the customers and whether or not claims were made. A random sample of 1200 customers from this company was investigated for 2020 and the results are shown in the table below.
Claim made in 2020No claim made in 2020Total
\multirow{3}{*}{Age}17-20 years24176200
21-50 years48652700
51 years and over14286300
Total8611141200
The data are to be used to determine whether or not making a claim is independent of age.
  1. Calculate the expected frequencies for the age group 51 years and over that
    1. made a claim in 2020
    2. did not make a claim in 2020 The 4 classes of customers aged between 17 and 50 give a value of \(\sum \frac { ( O - E ) ^ { 2 } } { E } = 7.123\) correct to 3 decimal places.
  2. Test, at the \(1 \%\) level of significance, whether or not making a claim is independent of age. Show your working clearly, stating your hypotheses, the degrees of freedom, the test statistic and the critical value used.
Edexcel S3 2023 June Q2
10 marks Moderate -0.3
  1. A business accepts cash, bank cards or mobile apps as payment methods.
The manager wishes to test whether or not there is an association between the payment amount and the payment method used. The manager takes a random sample of 240 payments and records the payment amount and the payment method used. The manager's results are shown in the table.
\multirow{2}{*}{}Payment amount
Under £50£50 to £150Over £150
\multirow{3}{*}{Payment method}Cash231918
Bank card213231
Mobile app163941
Using these results,
  1. calculate the expected frequencies for the payment amount under \(\pounds 50\) that
    1. use cash
    2. use a bank card
    3. use a mobile app Given that for the other 6 classes \(\sum \frac { ( O - E ) ^ { 2 } } { E } = 2.4048\) to 4 decimal places,
  2. test, at the \(5 \%\) level of significance, whether or not there is evidence for an association between the payment amount and the payment method used. You should state the hypotheses, the test statistic, the degrees of freedom and the critical value used for this test.