5 A medical researcher is investigating whether there is any relationship between the age of a person and the level of a particular protein in the person’s blood. She measures the levels of the protein (measured in suitable units) in a random sample of 12 hospital patients of various ages (in years). The spreadsheet shows the values obtained, together with a scatter diagram which illustrates the data.
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- The researcher decides that a test based on Pearson's product moment correlation coefficient may not be valid. Explain why she comes to this conclusion.
- Calculate the value of Spearman's rank correlation coefficient.
- Carry out a test based on this coefficient at the \(5 \%\) significance level to investigate whether there is any association between age and protein level.
- Explain why the researcher chose a sample that was random.
- The researcher had originally intended to use a sample size of 6 rather than the 12 that she actually used.
Explain what advantage there is in using the larger sample size.