confidence intervals. , hypothesis testing , critical Value

Question 1

The following table contains summary statistics on house sales in Canberra (by region) for the last 3 months.

The lake in the Centre of Canberra in Lake Burley Griffin. The first 3 regions in the table above (that is, Belconnen, Gungahlin and inner north) are north of the lake. The remaining regions are south of the lake.

Native Canberrans are friendly loyal to their side of the lake (that is, whether you live north or south lake burley). Those born and raised in north Canberra, tend to buy houses and retire in North Canberra, and would never consider moving south of the lake.

So how do Calculate the sample mean of house prices in North and South Canberra compare on house prices? You are going to use the summary statistics in the table above to assess whether there is sufficient evidence of a difference in the mean house price between North and South Canberra.

Note, for this question you may assume that:

1. The sample sizes in North and South Canberra are respectively large enough such that a t-test (of some sort) can be validly applied.

2. House prices are independent (that is, the sold price of one house is not affected by the sold price of any other house)

3. The houses that were sold in the last 3 months constitute a simple unbiased random sample of the houses within each region.

1. State the null (H0) and alternative (HA) hypotheses using proper statistical notation for the population parameters

2. Calculate the sample mean of house prices in North Canberra (that is, Belconnen, Gungahlin and inner north) (Please show your working by providing the equations you used to perform your calculation).

3. Calculate the sample mean of house prices in South Canberra (that is, Inner south, Molonglo Valley, Woden Valley, Weston Creek and Tuggeranong combined) (please show your working by providing the equations you used to perform your calculation).

4. The sample standard deviation of house prices in North and South Canberra are estimated to be $ 301250 and $476250 respectively. Will your test be a pooled-variance t-test or separate -variance t-test for the difference between two population means? Give a reason for your answer.

5. Calculate the value of your test statistic for this hypothesis test (Note: please show your working by providing the equation you used to calculate your test statistic)

6. Assuming a significance of =0.05，what critical Value(s) define your rejection region?

(Note: if your degree of freedom is greater than 120, you may obtain your critical Values from the standard normal distribution

1. Do you have statistical evidence to support your alternative hypothesis given the data? Why or why not? State your conclusion in the context of the equation.

2. Calculate the p-value of your test (as extra value or interval range for the p-value may be given)

(Please also provide the mathematical expression you used to calculate your p-value)