A real estate agent Irina Zubinina was asked to analyze the one-bedroom condo prices in the GTA. She took a random sample of 12 condos in Downtown Toronto and another random sample of 9 condos in Yorkville. The sample means (in $ thousands) are x1=742 for Downtown Toronto and x2=671 for Yorkville. Historically, the population standard deviations (in $ thousands) are 1=101 for Downtown Toronto and 2=64 for Yorkville. Could Irina Zubinina claim at a 3% 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,

zst=(x1x2)(12)21n1+22n2

Note: The nature of the distributions and availability of1

and 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.

H0

:

H1:

Which one is the claim?

• H1

(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.

zst=

(d) Does the test statistic fall into rejection region?

(e) What is the short version of your conclusion (in terms of H0 andH1

)?

• Fail to reject H0

and fail to support H1 and support H1 and reject H1 and fail to support H1 (claim) and support H1

• (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 3% level of significance, the sample data support the claim that the average price in Downtown Toronto is higher than the average price in Yorkville.
• At a 3% 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.

H0

(claim)

Reject H0

(claim)

Fail to support H0

(claim)

Reject H0

(claim)

Support H0