IB Questionbank

User interface language: English | Español

Date	May 2013	Marks available	2	Reference code	13M.2.sl.TZ1.1
Level	SL only	Paper	2	Time zone	TZ1
Command term	Show that	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.

[2]

Write down the number of degrees of freedom.

[1]

Write down the critical value for the test.

[1]

Show that the expected number of Medium Yield crops using Fertilizer C is 17, correct to the nearest integer.

[2]

Use your graphic display calculator to find for the data

(i) the \(\chi^2\) calculated value, \(\chi _{calc}^2\);

(ii) the p-value.

[3]

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

[2]

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.

Syllabus sections

Topic 4 - Statistical applications » 4.4 » The \({\chi ^2}\) test for independence: formulation of null and alternative hypotheses; significance levels; contingency tables; expected frequencies; degrees of freedom; \(p\)-values.

Show 143 related questions

18M.2.sl.TZ2.3e: State a conclusion for this test. Justify your answer.
18M.2.sl.TZ2.3d.ii: For this test find the p-value.
18M.2.sl.TZ2.3d.i: For this test state the null hypothesis.
18M.2.sl.TZ2.3c: Given that P(W > k) = 0.225 , find the value of k.
18M.2.sl.TZ2.3b.ii: Find the value of q.
18M.2.sl.TZ2.3b.i: Sketch a normal curve to represent this probability.
18M.2.sl.TZ2.3a.ii: In a training session there are 40 basketball players. Find the expected number of players...
18M.2.sl.TZ2.3a.i: Find the probability that a basketball player has a weight that is less than 61 kg.
18M.2.sl.TZ1.2h: Two flights are chosen at random from those which were slightly delayed. Find the...
18M.2.sl.TZ1.2f: Write down the probability that this flight arrived on time.
18M.2.sl.TZ1.2d.ii: Write down the associated p-value.
18M.2.sl.TZ1.2d.i: Write down the χ2 statistic.
18M.2.sl.TZ1.2a: State the alternative hypothesis.
18M.2.sl.TZ1.2b: Calculate the expected frequency of flights travelling at most 500 km and arriving slightly...
17N.2.sl.TZ0.1g: State the result of the test. Give a reason for your answer.
17N.2.sl.TZ0.1f.ii: Write down the \({\chi ^2}\) statistic.
17N.2.sl.TZ0.1f.i: Write down the \(p\)-value for the test;
17N.2.sl.TZ0.1e.ii: Write down the number of degrees of freedom.
17N.2.sl.TZ0.1e.i: Write down the null hypothesis for this test;
17N.2.sl.TZ0.1d: Find the expected frequency of students choosing the Science category and obtaining 31 to 40...
17N.2.sl.TZ0.1c.ii: Use your graphic display calculator to estimate the standard deviation of \(N\).
17N.2.sl.TZ0.1c.i: Use your graphic display calculator to estimate the mean of \(N\);
17N.2.sl.TZ0.1b.ii: Write down, for \(N\), the mid-interval value of the modal class.
17N.2.sl.TZ0.1b.i: Write down, for \(N\), the modal class;
17N.2.sl.TZ0.1a: State whether \(N\) is a discrete or a continuous variable.
18M.2.sl.TZ1.2e: State, with a reason, whether you would reject the null hypothesis.
16M.1.sl.TZ2.7c: State the conclusion of the test. Give a reason for your answer.
16M.1.sl.TZ2.7b: A \({\chi ^{\,2}}\) test at the \(5\,\% \) significance level is used to determine whether TV...
16M.1.sl.TZ2.7a: A survey was conducted among a random sample of people about their favourite TV show. People...
16M.1.sl.TZ1.10d: From the travellers taking part in the survey, 285 were 61 years or older and 420 preferred...
16M.1.sl.TZ1.10c: The critical value of this \(\chi {\,^2}\) test is \(21.026\). Use this information to write...
16M.1.sl.TZ1.10b: Find the number of degrees of freedom.
16M.1.sl.TZ1.10a: The manager of a travel agency surveyed 1200 travellers. She wanted to find out whether there...
10M.1.sl.TZ1.10a: State the null hypothesis, H0, for this test.
10M.1.sl.TZ1.10c: Of the 400 people Tony interviewed, 220 were male and 180 were female. 80 of the people had...
10M.1.sl.TZ1.10d: Tony used a 5 % level of significance for his test and obtained a p-value of 0.0634 correct...
10M.1.sl.TZ1.10b: Write down the number of degrees of freedom.
10M.1.sl.TZ2.9d: State whether the type of coffee drunk is independent of gender. Give a reason for your answer.
10M.1.sl.TZ2.9a.i: Write down the null hypothesis.
10M.1.sl.TZ2.9b: Write down the number of degrees of freedom for this test.
10M.1.sl.TZ2.9c: Write down the critical value for this test.
10N.2.sl.TZ0.1B.a: Write down the null hypothesis, H0, for this test.
10N.2.sl.TZ0.1B.b: Write down the number of degrees of freedom for this test.
10N.2.sl.TZ0.1B.d: Show that the expected number of females that have more than 5 meals per day is 13, correct...
10N.2.sl.TZ0.1B.e: Use your graphic display calculator to find the \(\chi _{calc}^2\) for this data.
10N.2.sl.TZ0.1B.f: Decide whether H0 must be accepted. Justify your answer.
10N.2.sl.TZ0.1B.c: Write down the critical value for this test.
12N.2.sl.TZ0.4c: The manager of the store wants to determine whether the screen size is independent of gender....
12N.2.sl.TZ0.4e: The manager of the store wants to determine whether the screen size is independent of gender....
12N.2.sl.TZ0.4f: The manager of the store wants to determine whether the screen size is independent of gender....
12N.2.sl.TZ0.4g: The manager of the store wants to determine whether the screen size is independent of gender....
12N.2.sl.TZ0.4b: The manager of the store wants to determine whether the screen size is independent of gender....
12N.2.sl.TZ0.4d: The manager of the store wants to determine whether the screen size is independent of gender....
12M.2.sl.TZ1.2d: Write down the critical value of \(\chi ^2\), at the 5 % level of significance.
12M.2.sl.TZ1.2f: Determine whether H0 should be accepted. Justify your answer.
12M.2.sl.TZ1.2a: Write down the null hypothesis, H0, for this test.
12M.2.sl.TZ1.2b: Find the expected value of female footballers.
12M.2.sl.TZ1.2c: Write down the number of degrees of freedom.
12M.2.sl.TZ1.2e: Use your graphic display calculator to determine the \(\chi _{calc}^2\) value.
12M.1.sl.TZ2.8a: Write down the null hypothesis.
12M.1.sl.TZ2.8b: The colours of the cars were red, green, blue, black and silver. Find the number of degrees...
12M.1.sl.TZ2.8c: At the 5 % significance level the \(\chi_{calc}^2\) was found to be 8.73. Write down the...
11N.2.sl.TZ0.2c: Pam decides to test her belief using a Chi-squared test at the \(5\% \) level of...
11N.2.sl.TZ0.2d: Write down (i) the Chi-squared calculated value; (ii) the number of degrees of...
11N.2.sl.TZ0.2e: State, giving a reason, whether there is sufficient evidence at the \(5\% \) level of...
09N.2.sl.TZ0.4B, c, i: The calculated value of \({\chi ^2}\) is \(1.367\) and the critical value of \({\chi ^2}\) is...
09N.2.sl.TZ0.4B, a: Write down the total number of male students.
09N.2.sl.TZ0.4B, b: Show that the expected frequency for males, whose favourite car colour is blue, is 12.6.
09M.1.sl.TZ1.6a: Find the number of degrees of freedom for the \(\chi^2\) test.
09M.1.sl.TZ1.6b: Write down the null hypothesis for the \(\chi^2\) test.
09M.1.sl.TZ1.6d: The critical value for the \(\chi^2\) test at the 5% significance level is 12.59. The...
11M.2.sl.TZ1.2B.d: A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether...
11M.2.sl.TZ1.2B.e: A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether...
11M.2.sl.TZ1.2B.f: A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether...
11M.2.sl.TZ1.2B.g: A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether...
09M.2.sl.TZ2.2i, b: For the number of fertilized plants with height greater than 75 cm, show that the expected...
09M.2.sl.TZ2.2i, c: Write down the value of \(\chi_{calc}^2\).
09M.2.sl.TZ2.2i, a: Write down the null and alternative hypotheses for this test.
09M.2.sl.TZ2.2i, d: Write down the number of degrees of freedom.
09M.2.sl.TZ2.2i, f: Is the manufacturer’s claim justified? Give a reason for your answer.
11M.2.sl.TZ2.1A.d: Use your graphic display calculator to find the \({\chi ^2}\) test statistic for this data.
13M.2.sl.TZ1.1b: Write down the number of degrees of freedom.
13M.2.sl.TZ1.1c: Write down the critical value for the test.
13M.2.sl.TZ1.1e: Use your graphic display calculator to find for the data (i) the \(\chi^2\) calculated...
11M.2.sl.TZ2.1A.e: State whether Ludmila accepts the null hypothesis. Give a reason for your answer.
11M.2.sl.TZ2.1A.c: Find the expected frequency for the females studying Spanish.
11M.2.sl.TZ2.1A.b: Write down the number of degrees of freedom.
11M.2.sl.TZ2.1A.a: State Ludmila’s null hypothesis.
13M.2.sl.TZ1.1a: State the null hypothesis, H0, for the test.
13M.2.sl.TZ1.1f: State the conclusion of the test. Give a reason for your decision.
13M.1.sl.TZ2.6a: Write down the null hypothesis.
13M.1.sl.TZ2.6b: Find the number of degrees of freedom for this test.
13M.1.sl.TZ2.6c: Write down the critical value for this test.
13M.1.sl.TZ2.6d: State the conclusion of this test. Give a reason for your decision.
07M.1.sl.TZ0.8a: Write a suitable null hypothesis for a \(\chi^2\) test on this data.
07M.1.sl.TZ0.8b: Write down the value of \(\chi^2\) for this data.
07M.1.sl.TZ0.8c: The number of degrees of freedom is 4. Show how this value is calculated.
07M.1.sl.TZ0.8d: The critical value, at the 5% level of significance, is 9.488. What conclusion can be drawn...
SPM.1.sl.TZ0.8a: Find the expected number of female volleyball players under this hypothesis.
SPM.1.sl.TZ0.8b: Write down the \(p\)-value for the test.
SPM.1.sl.TZ0.8c: State, with a reason, the conclusion of the test.
07N.2.sl.TZ0.4ii.a: Draw a table with 2 rows and 4 columns of data so that Manuel can perform a chi-squared test.
07N.2.sl.TZ0.4ii.c: Find the expected frequency for the number of females who had ‘Comedy’ as their most-watched...
07N.2.sl.TZ0.4ii.b: State Manuel’s null hypothesis and alternative hypothesis.
07N.2.sl.TZ0.4ii.d: Using your graphic display calculator, or otherwise, find the chi-squared statistic for...
07N.2.sl.TZ0.4ii.e: (i) State the number of degrees of freedom available for this calculation. (ii) State his...
08N.2.sl.TZ0.3a: Jorge applies a \({\chi ^2}\) test at the \(5\% \) level to investigate whether wearing a...
08M.1.sl.TZ1.5a: Write down the null hypothesis.
08M.1.sl.TZ1.5b: Write down the number of degrees of freedom.
08M.1.sl.TZ1.5c: Write down the chi-squared value.
08M.1.sl.TZ1.5d: State whether or not you will reject the null hypothesis, giving a clear reason for your answer.
08M.2.sl.TZ2.2i.c: The market research organization tests the survey data to determine whether the brand of...
08M.2.sl.TZ2.2i.d: The market research organization tests the survey data to determine whether the brand of...
08M.2.sl.TZ2.2i.e: The market research organization tests the survey data to determine whether the brand of...
08M.2.sl.TZ2.2i.f: The market research organization tests the survey data to determine whether the brand of...
08M.2.sl.TZ2.2i.g: The market research organization tests the survey data to determine whether the brand of...
09N.2.sl.TZ0.4B, c, ii: The calculated value of \({\chi ^2}\) is \(1.367\) and the critical value of \({\chi ^2}\) is...
09N.2.sl.TZ0.4B, c, iv: The calculated value of \({\chi ^2}\) is \(1.367\) and the critical value of \({\chi ^2}\) is...
10M.1.sl.TZ2.9a.ii: Write down the alternative hypothesis.
14M.1.sl.TZ2.8c: The \({\chi ^2}\) critical value is \(7.815\) at the \(5\%\) significance level. State...
14M.1.sl.TZ2.8a: Find the expected frequency for the females who use public transport to get to school.
14M.1.sl.TZ2.8b: Find the \({\chi ^2}\) statistic.
13N.1.sl.TZ0.8d: The critical value, at the \(5\%\) significance level, is \(7.815\). State, giving a reason,...
13N.1.sl.TZ0.8a: Write down the null hypothesis for this test.
13N.1.sl.TZ0.8b: Write down the number of degrees of freedom.
13N.1.sl.TZ0.8c: Write down the value of \(\chi _{calc}^2\).
14M.1.sl.TZ1.4a: State the null hypothesis.
14M.1.sl.TZ1.4b: Write down the number of degrees of freedom.
14M.1.sl.TZ1.4c: Write down (i) the \({\chi ^2}\) statistic; (ii) the associated p-value.
14M.1.sl.TZ1.4d: State, giving a reason, whether the null hypothesis should be accepted.
15M.1.sl.TZ2.7a: Write down the null hypothesis for this test.
15M.1.sl.TZ2.7b: Write down the observed number of viewers who preferred Rumba and were older than 20 years old.
15M.1.sl.TZ2.7c: Use your graphic display calculator to find the \(p\)-value for this test.
15M.1.sl.TZ2.7d: The producer claims that the type of Latin dance a viewer preferred is independent of their...
15M.2.sl.TZ1.1a: State (i) \({{\text{H}}_0}\), the null hypothesis for the test; (ii) ...
15M.2.sl.TZ1.1d: Find (i) the \({\chi ^2}\) statistic; (ii) the associated \(p\)-value for the test.
15M.2.sl.TZ1.1e: Determine, giving a reason, whether \({{\text{H}}_0}\) should be accepted.
15M.2.sl.TZ1.1b: Write down the number of degrees of freedom.
15M.2.sl.TZ1.1c: Show that the expected frequency of those between the ages of 26 and 40 who oppose the...
14N.1.sl.TZ0.10d: Minta found that the calculated value of the \({\chi ^2}\) test was 3.576. The critical value...
14N.1.sl.TZ0.10a: State Minta’s null hypothesis.
14N.1.sl.TZ0.10b: State the number of degrees of freedom.
14N.1.sl.TZ0.10c: 150 students showed a preference for a smoothie. Calculate the expected number of female...

Hide related questions

Question

Markscheme

Examiners report

Syllabus sections

View options