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

1. State your hypotheses clearly:

   • Null Hypothesis (H₀): ρ = 0 (no correlation)
   • Alternative Hypothesis (H₁): ρ < 0 (negative correlation)

2. Use a 5% level of significance: Using the significance level, the critical value for this test can be found from the correlation coefficient table for n=19, yielding a critical value of -0.387.

3. State the critical value used: The correlation coefficient calculated is -0.897. Since -0.897 < -0.387, we reject the null hypothesis and conclude that there is evidence of a significant negative correlation between x and y.

Using the equation provided:

y = -0.05 x + 1.92

We can express this equation in log form:

1. By substituting back we find: $log_{10} h = log_{10}(m^{k}) + log_{10}(a)$
   where $k = -0.05$ and $a = 10^{1.92}$. Therefore, we have:

   $h = a m^{k}$

   Now calculating values: a can be evaluated by: $a ext{ (approx. } = 83.2)$ Hence, the model for h on m is: $h ext{ (approx. } = 83.2 m^{-0.05})$