Determine the product moment correlation coefficient for these data.

Perform a two-tailed test, at the \(5\% \) level of significance, of the hypothesis that strength is independent of moisture content.

If the moisture content of a beam is found to be \(9.5\), use the appropriate regression line to estimate the strength of the beam.

\(r =  - 0.762\)     (M1)A1

Note:     Accept answers that round to \( - 0.76\).

[2 marks]

\({H_0}:\) Moisture content and strength are independent or \(\rho  = 0\)

\({H_1}:\) Moisture content and strength are not independent or \(\rho  \ne 0\)     A1

EITHER

test statistic is \(-3.33\)     A1

critical value is \(( \pm ){\text{ }}2.306\)     A1

since \( - 3.33 <  - 2.306\) or \(3.33 > 2.306\),     R1

reject \({H_0}\;\;\;\)(or equivalent)     A1

OR

\(p\)-value is \(0.0104\)     A2

as \(0.0104 < 0.05\),     R1

reject \({H_0}\;\;\;\)(or equivalent)     A1

Note:     The R1 and A1 can be awarded as follow through from their test statistic or \(p\)-value.

[5 marks]

\(x = {\text{strength}}\)

\(y = {\text{moisture content}}\)

\(x =  - 0.629y + 28.1\)     (M1)(A1)

if \(y = 9.5\) so \(x = 22.1\)     (M1)A1

Note:     Only accept answers that round to \(22.1\).

Note:     Award M1A1M0A0 for the other regression line \(y = 30.1 - 0.924x\).

[4 marks]

Total [11 marks]