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

Let:

• Null Hypothesis (H0): There is no significant negative correlation between x and y (ρ = 0).
• Alternative Hypothesis (H1): There is a significant negative correlation between x and y (ρ < 0).

Using a significance level of 5%, we compare our calculated correlation coefficient of -0.897 with the critical value of -0.387. Since -0.897 is less than -0.387, we reject the null hypothesis and conclude that there is evidence of a negative correlation.

To find a model for h on m in the form h = am^k, we start from the equation of the line:

y = -0.05x + 1.92

Substituting x = log10(m) and y = log10(h):

log10(h) = -0.05 log10(m) + 1.92

Taking 10 to the power on both sides gives:

h = 10^{(1.92)} imes m^{-0.05}

Thus, the model can be expressed as:

h = a * m^k, where a = 10^{(1.92)} and k = -0.05.

Calculating these values, we find: a ≈ 83.2 and k = -0.05.