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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