Question

# Suppose the average size of a new house built in a certain county in 2006 was...

Suppose the average size of a new house built in a certain county in 2006 was

2,271

square feet. A random sample of

30

new homes built in this county was selected in 2010. The average square footage was

2,187​,

with a sample standard deviation of

220

square feet.

 a. Using alphaαequals=0.10​, does this sample provide enough evidence to conclude that the average house size of a new home in the county has changed since​ 2006? b. Use technology to determine the​ p-value for this test.

a. Determine the null and alternative hypotheses. Choose the correct answer below.

A.

Upper H 0H0​:

μ=2,271

and

Upper H 1H1​:

μ≠2,271

B.

Upper H 0H0​:

μ≠2,271

and

Upper H 1H1​:

μ=2,271

C.

Upper H 0H0​:

μ=2,271

and

Upper H 1H1​:

μ>2,271

D.

Upper H 0H0​:

μ≥2,271

and

Upper H 1H1​:

μ<2,271

Determine the critical​ value(s).

The critical​ value(s) is(are)

nothing.

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

Determine the test​ statistic,

t Subscript x overbartx.

t Subscript x overbartxequals=nothing

​(Round to two decimal places as​ needed.)

What conclusion should be​ drawn? Choose the correct answer below.

A.

Suppose the average size of a new house built in a certain county in 2006 was

2 comma 2712,271

square feet. A random sample of

3030

new homes built in this county was selected in 2010. The average square footage was

2 comma 1872,187​,

with a sample standard deviation of

220220

square feet.

 a. Using alphaαequals=0.100.10​, does this sample provide enough evidence to conclude that the average house size of a new home in the county has changed since​ 2006? b. Use technology to determine the​ p-value for this test.

a. Determine the null and alternative hypotheses. Choose the correct answer below.

A.

Upper H 0H0​:

mu equals 2 comma 271μ=2,271

and

Upper H 1H1​:

mu not equals 2 comma 271μ≠2,271

B.

Upper H 0H0​:

mu not equals 2 comma 271μ≠2,271

and

Upper H 1H1​:

mu equals 2 comma 271μ=2,271

C.

Upper H 0H0​:

mu equals 2 comma 271μ=2,271

and

Upper H 1H1​:

mu greater than 2 comma 271μ>2,271

D.

Upper H 0H0​:

mu greater than or equals 2 comma 271μ≥2,271

and

Upper H 1H1​:

mu less than 2 comma 271μ<2,271

Determine the critical​ value(s).

The critical​ value(s) is(are)

nothing.

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

Determine the test​ statistic,

t Subscript x overbartx.

t Subscript x overbartxequals=nothing

​(Round to two decimal places as​ needed.)

What conclusion should be​ drawn? Choose the correct answer below.

A.

A.

RejectReject

the null hypothesis. The data

provideprovide

sufficient evidence to conclude that the average house size has changed since 2006.

B.

Do not rejectDo not reject

the null hypothesis. The data

provideprovide

sufficient evidence to conclude that the average house size has changed since 2006.

C.

RejectReject

the null hypothesis. The data

do not providedo not provide

sufficient evidence to conclude that the average house size has changed since 2006.

D.

Do not rejectDo not reject

the null hypothesis. The data

do not providedo not provide

sufficient evidence to conclude that the average house size has changed since 2006.

b. Use technology to determine the​ p-value for this test. What is the​ p-value?

​p-valueequals=nothing

​(Round to three decimal places as​ needed.)

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