IB Mathematics SL 4.11 Formulation of null and alternative hypotheses AI SL Paper 2 - Exam Style Questions - New Syllabus

(a)

Add all the values in the table:

\(15+10+12+16+11+14+13+12+10+21+11+5=150\)

So, the total number of classmates who replied is \(150\). A1

✅ Answer: \(150\)

(b)

For a \(\chi^2\) test for independence, the null hypothesis states that the two categories are independent.

\(H_0:\) The choice of main course is independent of the choice of ice cream flavour. A1

✅ Answer: Main course choice is independent of ice cream flavour choice.

(c)

Use a \(\chi^2\) test for independence with the observed-frequency table:

\(\begin{pmatrix}15&10&12&16\\11&14&13&12\\10&21&11&5\end{pmatrix}\)

Using a calculator or statistical software,

\(p=0.0926402\ldots\)

\(p=0.0926\) A2

✅ Answer: \(p=0.0926\)

(d)

Compare the \(p\)-value with the significance level \(0.05\):

\(0.0926>0.05\). R1

Since the \(p\)-value is greater than \(0.05\), there is insufficient evidence to reject the null hypothesis.

Therefore, there is insufficient evidence to say that main course choice is dependent on ice cream flavour choice. Equivalently, the data supports that the main course choice is independent of the ice cream flavour choice. A1

✅ Answer: There is insufficient evidence that the two choices are dependent.