| Date | May 2013 | Marks available | 2 | Reference code | 13M.2.sl.TZ1.1 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | State | Question number | 1 | Adapted from | N/A |
Question
An agricultural cooperative uses three brands of fertilizer, A, B and C, on 120 different crops. The crop yields are classified as High, Medium or Low.
The data collected are organized in the table below.
The agricultural cooperative decides to conduct a chi-squared test at the 1 % significance level using the data.
State the null hypothesis, H0, for the test.
Write down the number of degrees of freedom.
Write down the critical value for the test.
Show that the expected number of Medium Yield crops using Fertilizer C is 17, correct to the nearest integer.
Use your graphic display calculator to find for the data
(i) the \(\chi^2\) calculated value, \(\chi _{calc}^2\);
(ii) the p-value.
State the conclusion of the test. Give a reason for your decision.
Markscheme
The (crop) yield is independent of the (type of) fertilizer used. (A1)(A1)
Note: Award (A1) for (crop) yield and (type of) fertilizer, (A1) for “independent” or “not dependent” or “not associated”.
Do not accept “not correlated” or “not related” or “not connected” or “does not depend on”.
4 (A1)
13.277 (A1)(ft)
Note: Accept 13.3. Follow through from part (b).
\(\frac{{50}}{{120}} \times \frac{{40}}{{120}} \times 120\) or \(\frac{{50 \times 40}}{{120}}\) (M1)
Note: Award (M1) for correct substitution in the expected value formula.
= 16.6666... (A1)
= 17 (AG)
Note: Both unrounded and rounded answers must be seen to award (A1).
(i) \(\chi_{calc}^2 = 3.86 (3.86133...)\) (G2)
(ii) p-value \( = 0.425\) (\(0.425097...\)) (G1)
Since \(\chi_{calc}^2\) < Critical Value (R1)
Accept (do not reject) the Null Hypothesis. (A1)(ft)
Note: Accept decision based on p-value with comparison to 1 % (0.425097... > 0.01) . Do not award (R0)(A1). Follow through from parts (c) and (e). Numerical answers must be present in the question for a valid comparison to be made.
Examiners report
The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect terminology in the null hypothesis, (2) use of the \(5\%\) level, (3) an inability to find the expected value by hand, (4) comparison of incorrect values. Note, candidates will never be asked to calculate the chi-squared statistic other than from the GDC.
The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect terminology in the null hypothesis, (2) use of the \(5\%\) level, (3) an inability to find the expected value by hand, (4) comparison of incorrect values. Note, candidates will never be asked to calculate the chi-squared statistic other than from the GDC.
The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect terminology in the null hypothesis, (2) use of the \(5\%\) level, (3) an inability to find the expected value by hand, (4) comparison of incorrect values. Note, candidates will never be asked to calculate the chi-squared statistic other than from the GDC.
The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect terminology in the null hypothesis, (2) use of the \(5\%\) level, (3) an inability to find the expected value by hand, (4) comparison of incorrect values. Note, candidates will never be asked to calculate the chi-squared statistic other than from the GDC.
The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect terminology in the null hypothesis, (2) use of the \(5\%\) level, (3) an inability to find the expected value by hand, (4) comparison of incorrect values. Note, candidates will never be asked to calculate the chi-squared statistic other than from the GDC.
The great majority of candidates found this question to be a good start to the paper. The common errors were (1) incorrect terminology in the null hypothesis, (2) use of the \(5\%\) level, (3) an inability to find the expected value by hand, (4) comparison of incorrect values. Note, candidates will never be asked to calculate the chi-squared statistic other than from the GDC.
