6. 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.
| \cline { 2 - 6 }
\multicolumn{1}{c|}{} | | \(\sum \boldsymbol { h }\) | \(\sum \boldsymbol { h } ^ { 2 }\) | | Unbiased | | estimate of | | the mean |
| | Unbiased | | estimate of | | the variance |
|
| Exercise regularly | 50 | 3270 | 214676 | \(\alpha\) | \(\beta\) |
| 40 | 2832 | 201660 | 70.8 | 29.6 |
- Calculate the value of \(\alpha\) and the value of \(\beta\)
- Test, at the \(5 \%\) level of significance, whether there is evidence to support Amala's belief. State your hypotheses clearly.
- Explain the significance of the central limit theorem to the test in part (b).
- State two assumptions you have made in carrying out the test in part (b).