A real estate agent Irina Zubinina was asked to analyze the one-bedroom condo prices in the GTA. She took a random sample of 13 condos in High Park and another random sample of 20 condos in Distillery District. The sample means (in $ thousands) are x1=626x1=626 for High Park and x2=582x2=582 for Distillery District. Historically, the population standard deviations (in $ thousands) are 1=981=98 for High Park and 2=702=70 for Distillery District. Could Irina Zubinina claim at a 5% level of significance that the average price in High Park is higher than the average price in Distillery District? Use the zz-test for independent samples and the formula,

zst=(x1x2)(12)21n1+22n2zst=(x1-x2)-(1-2)12n1+22n2

Note: The nature of the distributions and availability of 11 and 22 allow us to use zz- approach, though both samples are comparatively small.

(a) State the null and alternative hypotheses, and identify which one is the claim. H0H0: Select an answer x - - x x - x - ? < = > H1H1: Select an answer - x x - x - x - ? < > = Which one is the claim?

• H1H1
• H0H0

(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 3 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=zst=

(d) Does the test statistic fall into rejection region? ? No Yes (e) What is the short version of your conclusion (in terms of H0H0 andH1H1)?

• Support H0H0 (claim) and support H1H1
• Reject H0H0 and support H1H1 (claim)
• Fail to support H0H0 and reject H1H1 (claim)
• Fail to reject H0H0 and fail to support H1H1 (claim)
• Reject H0H0 and fail to support H1H1 (claim)

(f) Select the correct statement.

• I have an evidence that the average price in High Park is the same or lower than the average price in Distillery District.
• At a 5% level of significance, the sample data support the claim that the average price in High Park is higher than the average price in Distillery District.
• At a 5% level of significance, there is not sufficient sample evidence to support the claim that the average price in High Park is higher than the average price in Distillery District.
• I proved that the average price in High Park is lower than the average price in Distillery District.