3 Pathology departments in hospitals routinely analyse blood specimens. Ideally the analysis should be done while the specimens are fresh to avoid any deterioration, but this is not always possible. A researcher decides to study the effect of freezing specimens for later analysis by measuring the concentrations of a particular hormone before and after freezing. He collects and divides a sample of 15 specimens. One half of each specimen is analysed immediately, the other half is frozen and analysed a month later. The concentrations of the particular hormone (in suitable units) are as follows.
| Immediately | 15.21 | 13.36 | 15.97 | 21.07 | 12.82 | 10.80 | 11.50 | 12.05 |
| After freezing | 15.96 | 10.65 | 13.38 | 15.00 | 12.11 | 12.65 | 12.48 | 8.49 |
| Immediately | 10.90 | 18.48 | 13.43 | 13.16 | 16.62 | 14.91 | 17.08 |
| After freezing | 9.13 | 15.53 | 11.84 | 8.99 | 16.24 | 14.03 | 16.13 |
A \(t\) test is to be used in order to see if, on average, there is a reduction in hormone concentration as a result of being frozen.
- Explain why a paired test is appropriate in this situation.
- State the hypotheses that should be used, together with any necessary assumptions.
- Carry out the test using a \(1 \%\) significance level.
- A \(p \%\) confidence interval for the true mean reduction in hormone concentration is found to be ( \(0.4869,2.8131\) ). Determine the value of \(p\).