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IB Maths AI SL 4.11 Hypothesis Testing Questions

Practise forming hypotheses, choosing significance levels, applying p-values or critical results and interpreting chi-square or t-test conclusions with assumptions.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation SL
Level
SL

Exam points

  • Form null and alternative hypotheses, choose a significance level and use a p-value or critical result to make a decision.
  • Use chi-square tests for independence/goodness of fit and t-tests for means with the stated sample assumptions.
  • Interpret the test conclusion in context, including Type I/II error implications, degrees of freedom and practical meaning.

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Study SL 4.11—Hypothesis testing conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AI SL 4.11 Hypothesis Testing Questions question 1

[Maximum number: 6]

Xavie conducted a study to see if there is a relationship between the price of an apartment, y, and its distance, x, from the city centre of Melbourne.
They took a random sample of six typical apartments along a train line in the city. Xavie obtained the data shown in the following table.

Table for Question IB Maths AI SL 4.11 Hypothesis Testing Questions question 1 — IB Maths AI SL

A plot of these data is seen in the following graph.

Figure for Question IB Maths AI SL 4.11 Hypothesis Testing Questions question 1 — IB Maths AI SL

Question (a)

(a)

Write down the alternative hypothesis.

[ 1 ]

Question (b)

(b)

Find the p-value for this test.

[ 2 ]

Question (c)

(c)

State the conclusion of the test. Justify your answer.

[ 2 ]

Question (d)

(d)

State one additional assumption Xavie has made about the distributions to conduct this test.

[ 1 ]
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