Anna is investigating the relationship between exercise and resting heart rate - Edexcel - A-Level Maths Statistics - Question 6 - 2022 - Paper 1

Let the null hypothesis be:

• H₀: ρ = 0 (No correlation) The alternative hypothesis is:
• H₁: ρ < 0 (There is a negative correlation)

Using the product moment correlation coefficient, which is -0.897, we will compare it with the critical value at a 5% significance level. The critical value for n = 19 (degrees of freedom = 17) is approximately -0.387. Since -0.897 < -0.387, we reject the null hypothesis and conclude that there is significant evidence of a negative correlation between x and y.

We can express the equation as:

$y = -0.05 imes ext{log}_{10}(m) + 1.92$

To find the model for h in terms of m, we start with

$y = ext{log}_{10}(h)$ Substituting the equation of the line of best fit gives us:

$ext{log}_{10}(h) = -0.05 imes ext{log}_{10}(m) + 1.92$ Taking the inverse logarithm:

$h = 10^{(-0.05 imes ext{log}_{10}(m) + 1.92)}$ Using the properties of logarithms, we have:

$h = 10^{1.92} imes m^{-0.05}$ Thus, we can express it in the form:

$h = a imes m^k$ where

• a = 10^{1.92} ext{ (approximately 83.21)}
• k = -0.05.