Diabetes tends to be more prevalent in urban populations, but why this is so is not fully understood. A recent study1 on mice was designed to investigate the link between diabetes and air pollution. The study involved mice, with randomly selected to have filtered air pumped into their cage while the other breathed particulate matter that simulated common air pollution. The response variable is the amount of insulin resistance each mouse had after weeks. Higher insulin resistance indicates a greater risk for developing diabetes. (a) Is this an observational study or randomized experiment?
A. Randomized experiment
B. Observational study
(b) If we are interested in whether there is a difference in mean insulin resistance between the two groups, what are the null and alternative hypotheses?

answer: do we write it

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

the correct answer is c

good luck love