| Date | May 2007 | Marks available | 2 | Reference code | 07M.1.sl.TZ0.8 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Give a reason | Question number | 8 | Adapted from | N/A |
Question
The local park is used for walking dogs. The sizes of the dogs are observed at different times of the day. The table below shows the numbers of dogs present, classified by size, at three different times last Sunday.
Write a suitable null hypothesis for a \(\chi^2\) test on this data.
Write down the value of \(\chi^2\) for this data.
The number of degrees of freedom is 4. Show how this value is calculated.
The critical value, at the 5% level of significance, is 9.488.
What conclusion can be drawn from this test? Give a reason for your answer.
Markscheme
H0: The size of dog is independent of the time of day, (or equivalent) (A1)
Award (A0) for ‘no correlation’ (C1)
[1 mark]
\(\chi^2 = 4.33\). (accept 4.328) (M1)(A1)
Note: GDC use is anticipated but candidates might calculate this by hand. (M1) can be awarded for a reasonable attempt to use the formula. (C2)
[2 marks]
\((3–1)(3–1) = 4\) (A1)
Award mark for left hand side seen. (C1)
[1 mark]
The hypothesis should not be rejected, (allow ‘accept H0’)
OR
The size of dog is independent of the time of day (A1)(ft)
\(4.33 < 9.488\) or \(0.363 > 0.05\) (R1)(ft)
Allow \(\chi_calc^2 < \chi_crit^2\) only if a value for \(\chi_calc^2\) is seen somewhere.
Note: Award (R1)(ft) for comparing the values and (A1)(ft) if the conclusion is valid according to the comparison given. If no reason is given, or if the reason is wrong both marks are lost. Note that (A0)(R1)(ft) can be awarded but (A1)(R0) cannot. (C2)
[2 marks]
Examiners report
a) Most of the students got the null hypothesis right but quite a few used the word correlation instead of independent.
b) Candidates who used a GDC got it correct, while those who tried valiantly to calculate it by hand generally got an M1 but A0.
c) Most of the students knew how to calculate the degrees of freedom.
d) Many students did not have a clear idea which values to compare in order to arrive at a conclusion for the chi-squared test. Many compared the significance level with either the chi-squared value or the critical value. Some did not reject the hypothesis but either gave no reason or the wrong one.
As mentioned above, quite a number of candidates did not appear to have been taught this part of the course. There were many non-attempts. It was not a difficult question as indicated by the large number of candidates who scored full marks.
a) Most of the students got the null hypothesis right but quite a few used the word correlation instead of independent.
b) Candidates who used a GDC got it correct, while those who tried valiantly to calculate it by hand generally got an M1 but A0.
c) Most of the students knew how to calculate the degrees of freedom.
d) Many students did not have a clear idea which values to compare in order to arrive at a conclusion for the chi-squared test. Many compared the significance level with either the chi-squared value or the critical value. Some did not reject the hypothesis but either gave no reason or the wrong one.
As mentioned above, quite a number of candidates did not appear to have been taught this part of the course. There were many non-attempts. It was not a difficult question as indicated by the large number of candidates who scored full marks.
a) Most of the students got the null hypothesis right but quite a few used the word correlation instead of independent.
b) Candidates who used a GDC got it correct, while those who tried valiantly to calculate it by hand generally got an M1 but A0.
c) Most of the students knew how to calculate the degrees of freedom.
d) Many students did not have a clear idea which values to compare in order to arrive at a conclusion for the chi-squared test. Many compared the significance level with either the chi-squared value or the critical value. Some did not reject the hypothesis but either gave no reason or the wrong one.
As mentioned above, quite a number of candidates did not appear to have been taught this part of the course. There were many non-attempts. It was not a difficult question as indicated by the large number of candidates who scored full marks.
a) Most of the students got the null hypothesis right but quite a few used the word correlation instead of independent.
b) Candidates who used a GDC got it correct, while those who tried valiantly to calculate it by hand generally got an M1 but A0.
c) Most of the students knew how to calculate the degrees of freedom.
d) Many students did not have a clear idea which values to compare in order to arrive at a conclusion for the chi-squared test. Many compared the significance level with either the chi-squared value or the critical value. Some did not reject the hypothesis but either gave no reason or the wrong one.
As mentioned above, quite a number of candidates did not appear to have been taught this part of the course. There were many non-attempts. It was not a difficult question as indicated by the large number of candidates who scored full marks.
