Suppose a random sample of 1,220 adults in a certain country were asked about their opinion regarding federal spending on public education. respondents were asked whether federal spending on public education was (a) too low, (b) adequate, or (c) too high. respondents were classified by income level. choose the correct hypotheses to test whether there is an association between the response to the question and income level.
a. upper h 0h0:
among adults in the country, opinions about federal spending on education and income level are associated.
upper h subscript aha:
among adults in the country, opinions about federal spending on education and income level are independent.
b. upper h 0h0:
there is no difference between the proportions of adults in the country who responded (a), (b) or (c) to the opinion question.
upper h subscript aha:
there is a difference between the proportions of adults in the country who responded (a), (b) or (c) to the opinion question.
c. upper h 0h0:
among adults in the country, opinions about federal spending on education and income level are independent.
upper h subscript aha:
among adults in the country, opinions about federal spending on education and income level are associated.
d. none of these

A. Upper H 0H0:

Among adults in the country, opinions about federal spending on education and income level are associated.

Upper H Subscript aHa:

Among adults in the country, opinions about federal spending on education and income level are independent.

Step-by-step explanation:

The null hypothesis (H0) is the statement that two phenomena are unrelated (the response and the income level). This hypothesis indicates that a population parameter (in this case, a parameter that represents association) is equal to a hypothetical value.

And the alternative hypothesis is what you expect to prove; that the two phenomena are related in some way. Normally, this hypothesis indicates that a population parameter (in this case, a parameter that represents association) is different from a value.

perimeter of the first rectangular board is 9 feet.

step-by-step explanation:

let p = perimeter of first board.

l = length of first board

w = width of first board

length of first board = 2 * width of first board - 3

l = 2w - 3

perimeter of first board = 2l + 2w

since l = 2w-3, then

p = 2*(2w-3) + 2w which equals 4w-6 + 2w which equals 6w-6

length and width of the second board are reciprocals of corresponding length and width of the first board.

length of second board = 1/(2w-3)

width of second board = 1/w

perimeter of second board is 1/5th perimeter of the first board.

perimeter of second board = p/5

perimeter of the second board = (2/(2w-3) + 2/w)

since the perimeter of the first board is 5 times the perimeter of the second board, this means that:

6w-6 = 5*(2/(2w-3) + 2/w)

which is the same as:

6w-6 = (10/(2w-3) + 10/w)

if we multiply both sides of this equation by (2w-3), we get:

(6w-6)*(2w-3) = 10 + 10*(2w-3)/w

if we multiply both sides of this equation by w, we get:

(6w-6)*(2w-3)*w = 10*w + 10*(2w-3)

we can simplify this to become:

(6w-6)*(2w-3)*w = 10w + 20w - 30

which becomes:

(6w-6)*(2w-3)*w = 30w-30

if we divide both sides of this equation by (6w-6), we get:

(2w-3)*w = (30w-30)/(6w-6)

which becomes:

(2w-3)*w = 5

this can be simplified to:

2w^2 - 3w = 5

subtract 5 from both sides of this equation to get:

2w^2 - 3w - 5 = 0

which can be factored into:

(2w-5)*(w+1) = 0

which makes:

w = 5/2

or

w = -1.

w can't be negative so the only possible answer is w = 5/2.

if w = 5/2, then

p = 2w-3 = 5-3 = 2

we have:

p = 2

w = 5/2

p = 2l + 2w gets p = 4 + 5 = 9

the perimeter of the first board is 9 feet.

since the perimeter of the second board is 1/5 the perimeter of the first board, the perimeter of the second board is 9/5.

to see if that's correct, we substitute known values for l and w into the second board.

the length of the second board is 1/l.

this becomes 1/2.

the width of the second board is 1/w

this bgecomes 1/(5/2) = (2/5)

let l2 = length of second board.

let w2 = width of second board.

l2 = (1/2)

w2 = (2/5)

let p2= perimeter of second board.

then p2 = 9/5

since p2 = 2*l2 + 2*w2, we should get p2 = 9/5 using the dimensions of l2 and w2.

2 * l2 = 2 * (1/2) = 1

2 * w2 = 2 * (2/5) = 4/5

1 is the same as 5/5

5/5 + 4/5 = 9/5

p2 checks out good.

the dimensions as given are good.

answer to the problem is:

perimeter of the first rectangular board is 9 feet.