A real estate agent Jennifer Nguyen was asked to analyze the one-bedroom condo prices in the GTA. She took a random sample of 9 condos in Downtown Toronto and another random sample of 6 condos in Yorkville. The sample means (in $ thousands) are ¯ x 1 = 739 for Downtown Toronto and ¯ x 2 = 668 for Yorkville. Historically, the population standard deviations (in $ thousands) are σ 1 = 99 for Downtown Toronto and σ 2 = 62 for Yorkville. Could Jennifer Nguyen claim at a 1% level of significance that the average price in Downtown Toronto is higher than the average price in Yorkville? Use the z -test for independent samples and the formula, z s t = ( ¯ x 1 − ¯ x 2 ) − ( μ 1 − μ 2 ) √ σ 2 1 n 1 + σ 2 2 n 2 Note: The nature of the distributions and availability of σ 1 and σ 2 allow us to use z - approach, though both samples are comparatively small. (a) State the null and alternative hypotheses, and identify which one is the claim. H 0 : Select an answer ? H 1 : Select an answer ? Which one is the claim? H 1 H 0 (b) Find the critical value(s). In the first box please indicate the sign(s), and in the second box enter the numeric value. In part (b) your answer should contain 2 decimal places. Critical Value(s) = ? (c) What is the test statistic? For part (c), use the correct sign for the test statistic and round your answer to 3 decimal places. z s t = (d) Does the test statistic fall into rejection region? ? (e) What is the short version of your conclusion (in terms of H 0 and H 1 )? Fail to reject H 0 and fail to support H 1 (claim) Fail to support H 0 and reject H 1 (claim) Reject H 0 and support H 1 (claim) Support H 0 (claim) and support H 1 Reject H 0 and fail to support H 1 (claim) (f) Select the correct statement. I have an evidence that the average price in Downtown Toronto is the same or lower than the average price in Yorkville. At a 1% level of significance, there is not sufficient sample evidence to support the claim that the average price in Downtown Toronto is higher than the average price in Yorkville. I proved that the average price in Downtown Toronto is lower than the average price in Yorkville. At a 1% level of significance, the sample data support the claim that the average price in Downtown Toronto is higher than the average price in Yorkville.
A real estate agent Jennifer Nguyen was asked to analyze the one-bedroom condo prices in the GTA. She took a random sample of 9 condos in Downtown Toronto and another random sample of 6 condos in Yorkville. The sample means (in $ thousands) are
¯
x
1
=
739
for Downtown Toronto and
¯
x
2
=
668
for Yorkville. Historically, the population standard deviations (in $ thousands) are
σ
1
=
99
for Downtown Toronto and
σ
2
=
62
for Yorkville. Could Jennifer Nguyen claim at a 1% level of significance that the average price in Downtown Toronto is higher than the average price in Yorkville? Use the
z
-test for independent samples and the formula,
z
s
t
=
(
¯
x
1
−
¯
x
2
)
−
(
μ
1
−
μ
2
)
√
σ
2
1
n
1
+
σ
2
2
n
2
Note: The nature of the distributions and availability of
σ
1
and
σ
2
allow us to use
z
- approach, though both samples are comparatively small.
(a) State the null and alternative hypotheses, and identify which one is the claim.
H
0
:
Select an answer
?
H
1
:
Select an answer
?
Which one is the claim?
H
1
H
0
(b) Find the critical value(s). In the first box please indicate the sign(s), and in the second box enter the numeric value.
In part (b) your answer should contain 2 decimal places.
Critical Value(s) =
?
(c) What is the test statistic?
For part (c), use the correct sign for the test statistic and round your answer to 3 decimal places.
z
s
t
=
(d) Does the test statistic fall into rejection region?
?
(e) What is the short version of your conclusion (in terms of
H
0
and
H
1
)?
Fail to reject
H
0
and fail to support
H
1
(claim)
Fail to support
H
0
and reject
H
1
(claim)
Reject
H
0
and support
H
1
(claim)
Support
H
0
(claim) and support
H
1
Reject
H
0
and fail to support
H
1
(claim)
(f) Select the correct statement.
I have an evidence that the average price in Downtown Toronto is the same or lower than the average price in Yorkville.
At a 1% level of significance, there is not sufficient sample evidence to support the claim that the average price in Downtown Toronto is higher than the average price in Yorkville.
I proved that the average price in Downtown Toronto is lower than the average price in Yorkville.
At a 1% level of significance, the sample data support the claim that the average price in Downtown Toronto is higher than the average price in Yorkville.
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