Question

Exercise 1.21 introduces a study examining whether or not noses continue to grow throughout a person's lifetime. The study included many measurements (including size of the nose as measured by total volume) and included multiple tests. Exercises 4.98 to 4.100 each describe one of the tests along with information about the p-value for that test. In each case:

• (a)State the hypotheses.
• (b)Give the formal decision using a 5% significance level, and interpret the conclusion in context.

1)In a test to see whether males, on average, have bigger noses than females, the study indicates that “p < 0.01.”

2)In a test to see whether there is a positive linear relationship between age and nose size, the study indicates that “p < 0.001.”

Answer 1

(a) Hypothesis: Males generally have bigger noses than females i.e. H₀: m₁>m₂where m₁denotes the average size of nose of males and m₂denotes the average size of nose of females

Since p<0.01, this suggests that the hypothesis (a) should be rejected at 5% level of significance(p< 0.05) and it can be concluded that males do not have bigger noses than females.

(b) Hypothesis: There is a positive linear relationship between age and nose size i.e. H₀: r > 0 where r denotes the correlation coefficient between age and nose size.

Since p < 0.001, this suggests that the hypothesis (b) should also be rejected at 5% level of significance(p< 0.05) and it can be concluded that there is no positive linear relationship between age and nose size.