| Date | May 2017 | Marks available | 5 | Reference code | 17M.3sp.hl.TZ0.5 |
| Level | HL only | Paper | Paper 3 Statistics and probability | Time zone | TZ0 |
| Command term | Calculate | Question number | 5 | Adapted from | N/A |
Question
A teacher decides to use the marks obtained by a random sample of 12 students in Geography and History examinations to investigate whether or not there is a positive association between marks obtained by students in these two subjects. You may assume that the distribution of marks in the two subjects is bivariate normal.
He gives the marks to Anne, one of his students, and asks her to use a calculator to carry out an appropriate test at the 5% significance level. Anne reports that the \(p\)-value is 0.177.
State suitable hypotheses for this investigation.
State, in context, what conclusion should be drawn from this \(p\)-value.
The teacher then asks Anne for the values of the \(t\)-statistic and the product moment correlation coefficient \(r\) produced by the calculator but she has deleted these. Starting with the \(p\)-value, calculate these values of \(t\) and \(r\).
Markscheme
\({H_0}:\rho = 0;{\text{ }}{H_1}:\rho > 0\) A1
Note: Do not accept \(r\) in place of \(\rho \).
[1 mark]
insufficient evidence to conclude that there is a (positive) association between marks in these two subjects (or equivalent statement in context) A1
[1 mark]
degrees of freedom \( = 10\) (A1)
required value of \(t = {\text{inverse }}t(0.823)\) (M1)
\( = 0.972\) A1
attempt to solve \(t = r\sqrt {\frac{{n - 2}}{{1 - {r^2}}}} \) (M1)
\(r = 0.294\) A1
Note: Accept any \(r\) value that rounds to 0.29.
Note: Follow through their \(t\) value to determine \(r\).
[5 marks]
