A USA Today/Gallup poll asked a group of unemployed and underemployed Americans if they have had major problems in their relationships with their spouse or another close family member as a result of not having a job (if unemployed) or not having a full-time job (if underemployed). 27% of the 1,145 unemployed respondents and 25% of the 675 underemployed respondents said they had major problems in relationships as a result of their employment status. (a) What are the hypotheses for evaluating if the proportions of unemployed and underemployed people who had relationship problems were different

Null hypothesis: H₀: p₁ = p₂.

Alternate hypothesis: H₀: p₁ ≠ p₂.

Step-by-step explanation:

A statistical experiment is conducted to determine whether the proportions of unemployed and underemployed people who had relationship problems were different.

Let p₁ = the proportion of unemployed people who had relationship problems and p₂ = the proportion of underemployed people who had relationship problems.

A hypothesis test for difference between proportions, can be conducted to determine if there is any difference between the two population proportions.

Use a z-test for the test statistic.

The hypothesis test is:

H₀: There is no difference between the proportions of unemployed and underemployed people who had relationship problems, i.e. p₁ = p₂.

Hₐ: There is a significant difference between the proportions of unemployed and underemployed people who had relationship problems, i.e. p₁ ≠ p₂.

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