IB Maths AI SL 4.11 Hypothesis testing

IB Mathematics: applications and interpretation guide, first assessment 2021

Students practise conducting hypothesis tests—including chi-squared, t-, and binomial tests—and writing conclusions in context.

How this is tested

state H₀ and H₁ correctly—e.g., H₀: φ = 0.45, H₁: φ > 0.45 for a one-tailed binomial proportion test
use a chi-squared test for independence and interpret the p-value
choose the correct test by matching the statistical context and data type

[Maximum number: 7]

Dr Petrillo wrote a short scientific essay. He analysed the readability of his essay by counting the number of letters in each word.
Dr Petrillo constructs a box and whisker diagram for his data.

(a)

Write down the alternative hypothesis for this test.

[ 1 ]

(b)

The observed and expected frequencies of the number of letters in each word in his essay are listed in the following table.

Table for Question 1(e) — IB Maths AI SL

[ 4 ]

(i)

Write down the number of degrees of freedom.

(ii)

Find the $\chi^{2}$ statistic for this test.

(iii)

Find the p-value for this test.

The critical value for this test, at the 1 % significance level, is 16.812 .

[ 4 ]

(c)

State whether Dr Petrillo should reject the null hypothesis. Justify your answer.

[ 2 ]

How this is tested

Question 1

Question 1(d)

Question 1(e)

Question 1(e)(i)

Question 1(e)(ii)

Question 1(e)(iii)

Question 1(f)