Next time you see an elderly man, check out his nose and ears! While most parts of the human body stop growing as we reach adulthood, studies show that noses and ears continue to grow larger throughout our lifetime. In one study 1 examining noses, researchers report "Age significantly influence all analyzed measurements:" including volume, surface area, height, and width of noses. The gender of the 859 participants in the study was also recorded, and the study reports that "male increments in nasal dimensions were larger than female ones."the study indicates that "p<0.01."

a. State the hypotheses. Your answer should be an expression composed of symbols

b. Interpret the conclusion in context.
i. We have evidence that males have bigger noses than females, on average.
ii. We do not have evidence that males have bigger noses than females, on average.
iii. We have evidence that males and females have the same size noses, on average.
iv. We do not have evidence that males and females have the same size noses, on average.

In a sample of 859 participants, the gender and the nasal dimensions were recorded and the "increase of nasal dimensions" was compared between the two genders. To compare two populations the best is to do so trough the population means.

Be X₁: nasal dimensions of male participants, and X₂: nasal dimensions of female participants, the hypotheses are:

a.

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

If the p-value is p<0.01 at, for example, α:0.05, the decision is to reject the null hypothesis. If so the conclusion is that the average nasal dimension of males is greater than the average nasal dimension of females.

b.

The correct option is:

i. We have evidence that males have bigger noses than females, on average.

I hope you have a SUPER day!