Problem

Amala believes that the resting heart rate is lower in men who exercise regularly compared to men who do not exercise regularly. She measures the resting heart rate, $h$, of a random sample of 50 men who exercise regularly and a random sample of 40 men who do not exercise regularly. Her results are summarised in the table below.

Sample	Sample size	$\sum h$	$\sum h^2$	Unbiased estimate of the mean	Unbiased estimate of the variance
Exercise regularly	50	3270	214676	$\alpha$	$\beta$
Do not exercise regularly	40	2832	201660	70.8	29.6

(a) Calculate the value of $\alpha$ and the value of $\beta$

(b) Test, at the 5% level of significance, whether there is evidence to support Amala’s belief. State your hypotheses clearly.

(c) Explain the significance of the central limit theorem to the test in part (b).

(d) State two assumptions you have made in carrying out the test in part (b).