A study was done to test the notion that people are taller when they first wake up in the morning than in the evening right before they go to bed. To test this theory, the heights of children in a boarding school in India were measured. Values were recorded (in mm) for each child in the morning and again in the evening. The data is recorded in AMPM-Heights. xlsx You want to determine if the children are taller in the morning than in the evening. Define the differences as AM Height minus PM Height. Required:
Compute a 95% confidence interval for the true mean difference of heights.

step-by-step explanation:

i am not sure sorry : c

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