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Inferential Statistics · Paper 2 — Free Maths AI SL Practice Questions

What this topic covers

This is the topic examiners lean on hardest, because it's the one place they can test whether you actually understand what a number means, not just whether you can press the right calculator button. A GDC will hand you $r$ , a $p$ -value, or a confidence interval in seconds — the marks live in knowing which tool to reach for, reading the question for the tail direction, and finishing with a sentence back in context. Four threads run through it: describing data you already have, inferring about a population you don't, modelling chance for single events, and modelling chance across a whole range of outcomes. They constantly borrow from each other, so treat this as one connected chapter, not four separate ones.

Read the full Statistics and Probability lesson notes →

1MasterySAQ-SRegression analysis6 marksPaper 2~9 min

The owner of a small bakery records the number of hours of sunshine,

h

, and the daily sales of iced coffee,

s

(in cups), over 8 randomly selected summer days.

h

(hours) —

4.2

—

5.1

—

6.8

—

7.3

—

8.0

—

9.5

—

10.2

—

11.4

s

(cups) —

18

—

22

—

31

—

35

—

38

—

47

—

51

—

58

(a)

Calculate the Pearson product-moment correlation coefficient,

r

, for this data. [1 mark]

(b)

Determine the equation of the regression line of

s

h

, giving your answer in the form

s = a + bh

, where

a

and

b

are correct to 3 significant figures. [2 marks]

(c)

Calculate an estimate for the number of cups of iced coffee sold when there are

9.0

hours of sunshine. [1 mark]

(d)

Evaluate the reliability of your estimate in part (c), justifying your answer with reference to both the value of

r

and the data range. [2 marks]

Solutions

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