3. A researcher hypothesizes that the lowering of cholesterol is associated with dieting.

To test this, the researcher recruited 20 men aged 40–50 years and measured their cholesterol levels before and after dieting for 3 weeks (assuming the difference follows the normal distribution). The difference is calculated, which is non-significant

(p=0.09) compared to zero in a two-sided test at the  =0.05 level.

(a) Can you figure out how to perform a significance test using what you have learnt in this chapter? State H0 and H1 for this test.

(b) Interpret in your own words what the p value and  level means in this case.

What are their differences?

(c) Can the researcher claim that the probability that H0 is true is 0.09? Why?

(d) Can the researcher claim that diet has no effect?

(e) What is the advantage of a one-sided test? Is it appropriate if the researcher decides to select the critical value of a one-sided test after a two-sided value p=0.09 has been obtained? Why?

(f) Is it appropriate to select a more liberal  (say, 0.1) after the researcher found a p value of 0.09 if it was nonsignificant at a significance level of 0.05.