A survey was conducted among a random sample of people about their favourite TV show. People were classified by gender and by TV show preference (Sports, Documentary, News and Reality TV).

The results are shown in the contingency table below.

Find the expected number of females who prefer documentary shows.

A \({\chi ^{\,2}}\) test at the \(5\,\% \) significance level is used to determine whether TV show preference is independent of gender.

Write down the \(p\)-value for the test.

State the conclusion of the test. Give a reason for your answer.

\(\frac{{54}}{{180}} \times \frac{{93}}{{180}} \times 180\)   OR \(\frac{{54 \times 93}}{{180}}\)          (M1)

\( = 27.9\)            (A1)    (C2)

\(0.0321\,\,\,(0.032139...)\)               (A2)   (C2)

TV show preference is not independent of gender           (A1)(ft)

OR

reject the null hypothesis           (A1)(ft)

\(0.0321 < 0.05\)           (R1)    (C2)

Notes: Accept TV show preference is dependent on gender. Accept “associated”. Do not accept “correlated” or “related” or “linked”.
Award (R1) for the comparison, (A1)(ft) for a consistent conclusion with their answer to part (b). It is possible that (A0)(R1) be awarded.
Do not award (A1)(R0).

Question 7: \({\chi ^{\,2}}\) test.

Candidates used their GDC to find the expected frequency with varying success whereas the \(p\)-value of the \({\chi ^{\,2}}\) test was usually correct; with some losing as many as four marks for giving answers to 1 significant figure with no working. As in the specimen paper the null hypotheses was not stated and so it was necessary to state what was being rejected. Candidates should write an explicit numerical comparison between \(p\) value and significance level to justify whether the null hypothesis is rejected or not. Amongst the candidates that made a comparison often the inequality sign was the wrong direction or the candidate made an inconsistent conclusion. There were many instances of poor mathematical terminology with correlation and independence used interchangeably likewise when candidates compared the significance level with their calculated \({\chi ^{\,2}}\) value.

Question 7: \({\chi ^{\,2}}\) test.

Candidates used their GDC to find the expected frequency with varying success whereas the \(p\)-value of the \({\chi ^{\,2}}\) test was usually correct; with some losing as many as four marks for giving answers to 1 significant figure with no working. As in the specimen paper the null hypotheses was not stated and so it was necessary to state what was being rejected. Candidates should write an explicit numerical comparison between \(p\) value and significance level to justify whether the null hypothesis is rejected or not. Amongst the candidates that made a comparison often the inequality sign was the wrong direction or the candidate made an inconsistent conclusion. There were many instances of poor mathematical terminology with correlation and independence used interchangeably likewise when candidates compared the significance level with their calculated \({\chi ^{\,2}}\) value.

Question 7: \({\chi ^{\,2}}\) test.

Candidates used their GDC to find the expected frequency with varying success whereas the \(p\)-value of the \({\chi ^{\,2}}\) test was usually correct; with some losing as many as four marks for giving answers to 1 significant figure with no working. As in the specimen paper the null hypotheses was not stated and so it was necessary to state what was being rejected. Candidates should write an explicit numerical comparison between \(p\) value and significance level to justify whether the null hypothesis is rejected or not. Amongst the candidates that made a comparison often the inequality sign was the wrong direction or the candidate made an inconsistent conclusion. There were many instances of poor mathematical terminology with correlation and independence used interchangeably likewise when candidates compared the significance level with their calculated \({\chi ^{\,2}}\) value.