Standard +0.3 This is a standard three-part correlation question requiring routine application of formulas: calculating PMCC from summary statistics, finding a regression line estimate, and performing a hypothesis test for correlation. While it involves multiple steps and careful arithmetic, all techniques are textbook procedures with no novel problem-solving required, making it slightly easier than average for Further Maths.
10 The lengths, \(x \mathrm {~m}\), and masses, \(y \mathrm {~kg}\), of 12 randomly chosen babies born at a particular hospital last year are summarised as follows.
$$\Sigma x = 7.50 \quad \Sigma x ^ { 2 } = 4.73 \quad \Sigma y = 38.6 \quad \Sigma y ^ { 2 } = 124.84 \quad \Sigma x y = 24.25$$
Find the value of the product moment correlation coefficient for this sample.
Obtain an estimate for the mass of a baby, born last year at the hospital, whose length is 0.64 m .
Test, at the \(2 \%\) significance level, whether there is non-zero correlation between the two variables.
10 The lengths, $x \mathrm {~m}$, and masses, $y \mathrm {~kg}$, of 12 randomly chosen babies born at a particular hospital last year are summarised as follows.
$$\Sigma x = 7.50 \quad \Sigma x ^ { 2 } = 4.73 \quad \Sigma y = 38.6 \quad \Sigma y ^ { 2 } = 124.84 \quad \Sigma x y = 24.25$$
Find the value of the product moment correlation coefficient for this sample.
Obtain an estimate for the mass of a baby, born last year at the hospital, whose length is 0.64 m .
Test, at the $2 \%$ significance level, whether there is non-zero correlation between the two variables.
\hfill \mbox{\textit{CAIE FP2 2013 Q10 [11]}}