A research center reports on a survey taken in which they asked whether respondents have heard "good news" about the job market. They compared those making

$30,000

or less per year with those making between

$31,000

and

$74,000.

We'll label the population of those making less than

$30,000

as population 1 (low income), and those making between

$31,000

and

$74,000

as population 2 (middle income). A

90%

confidence interval for the difference in proportions, 1 (low) minus 2 (middle) is

(−0.09,0.05).

Interpret this confidence interval. If the interval contains 0, indicate what this means. Explain the meaning of positive and/or negative values.

I am 90% confident

I am 10% confident

There is a 10% chance

There is a 90% chance

I am 95% confident

that the difference in

population proportions

population proportions

sample proportions

sample standard deviations

population standard deviations

(low income−middle income)

is between

negative 0.09−0.09

and

0.050.05.

(Type integers or decimals. Do not round. Use ascending order.)

The interval

captures

captures

does not capture

0, suggesting that it

is

is

is not

plausible that

the population proportions are the same.

the samples came from the same population.

the population proportions are the same.

the population standard deviations are the same

one of the population proportions is 0.

Since the boundary values

have opposite signs,

are both negative,

are both positive,

have opposite signs,

we

cannot conclude that a different

can conclude that a lesser

cannot conclude that a different

can conclude that a greater

percentage of low-income individuals have heard "good news" about the job market compared to middle-income individuals.