The manager of a travel agency surveyed 1200 travellers. She wanted to find out whether there was a relationship between a traveller’s age and their preferred destination. The travellers were asked to complete the following survey.

A \(\chi {\,^2}\) test was carried out, at the \(5\% \) significance level, on the data collected.

Write down the null hypothesis.

Find the number of degrees of freedom.

The critical value of this \(\chi {\,^2}\) test is \(21.026\).

Use this information to write down the values of the \(\chi {\,^2}\) statistic for which the null hypothesis is rejected.

From the travellers taking part in the survey, 285 were 61 years or older and 420 preferred Tokyo.

Calculate the expected number of travellers who preferred Tokyo and were 61 years or older.

age and preferred destination are independent        (A1) (C1)

Note: Accept there is no association between preferred destination and age. Accept not dependent. Do not accept “not related” or “not correlated” or “influenced”.

\((4 - 1) \times (5 - 1)\)       (M1)

Note: Award (M1) for \(3\) and \(4\) (\(4 - 1\) and \(5 - 1\)) seen.

\( = 12\)       (A1) (C2)

\(\chi \,_{calc}^2\, > 21.026\,\)  OR \((21.026,\,\,\infty )\)  OR \(]21.026\,,\,\,\infty [\)       (A1) (C1)

Note: Do not accept \(\chi \,_{calc}^2\, > \chi \,_{crit}^2\) without numerical value.

\(\frac{{285}}{{1200}} \times \frac{{420}}{{1200}} \times 1200\,\,\,\,\,\,\left( {\frac{{285 \times 420}}{{1200}}} \right)\)       (M1)

Note: Award (M1) for correct substitution into correct formula.

\( = 99.8\,\,\,(99.75)\)       (A1) (C2)

Question 10: \(\chi {\,^2}\) test
Without doubt, this question was the subject of most comment in the feedback from teachers; opinion was divided between those who wanted the straightforward formulaic approach that can be taught in a recipe-book manner and those who saw the critical thinking nature of the question’s intent; being able to take the data, set up the two-way table and design the test. These are necessary skills for the IA project and they should be transferrable to an examination. That said, the unfamiliar form of the question caught a number of candidates unaware, most noticeably in the statement of the critical region; which is still felt – despite the GDC’s use of the \(p\)-value – to be an important concept that should be introduced to candidates and will continue to be tested. Calculating the degrees of freedom was also subject to many errors.

Question 10: \({\chi ^2}\) test Without doubt, this question was the subject of most comment in the feedback from teachers; opinion was divided between those who wanted the straightforward formulaic approach that can be taught in a recipe-book manner and those who saw the critical thinking nature of the question’s intent; being able to take the data, set up the two-way table and design the test. These are necessary skills for the IA project and they should be transferrable to an examination. That said, the unfamiliar form of the question caught a number of candidates unaware, most noticeably in the statement of the critical region; which is still felt – despite the GDC’s use of the \(p\)-value – to be an important concept that should be introduced to candidates and will continue to be tested. Calculating the degrees of freedom was also subject to many errors.

Question 10: \(\chi {\,^2}\) test Without doubt, this question was the subject of most comment in the feedback from teachers; opinion was divided between those who wanted the straightforward formulaic approach that can be taught in a recipe-book manner and those who saw the critical thinking nature of the question’s intent; being able to take the data, set up the two-way table and design the test. These are necessary skills for the IA project and they should be transferrable to an examination. That said, the unfamiliar form of the question caught a number of candidates unaware, most noticeably in the statement of the critical region; which is still felt – despite the GDC’s use of the \(p\)-value – to be an important concept that should be introduced to candidates and will continue to be tested. Calculating the degrees of freedom was also subject to many errors.

Question 10: \({\chi ^2}\) test Without doubt, this question was the subject of most comment in the feedback from teachers; opinion was divided between those who wanted the straightforward formulaic approach that can be taught in a recipe-book manner and those who saw the critical thinking nature of the question’s intent; being able to take the data, set up the two-way table and design the test. These are necessary skills for the IA project and they should be transferrable to an examination. That said, the unfamiliar form of the question caught a number of candidates unaware, most noticeably in the statement of the critical region; which is still felt – despite the GDC’s use of the \(p\)-value – to be an important concept that should be introduced to candidates and will continue to be tested. Calculating the degrees of freedom was also subject to many errors.