Question

A random sample of 9 recently sold homes in a local market collects the list price and selling price for each house. The prices are listed below in thousands of dollars. A group of realtors wants to test the claim that houses are selling for more than the list price.

List Price	490	275	289	349	460	499	325	380	299
Sell Price	485	275	280	360	465	490	340	395	315

(a) Find d¯, the mean of the differences.

(b) State the claim, the negation of the claim, H₀, and H₁ (using equations and the parameter μd).

(c) Find the p-value. Use a significance level of α=.05 to test the claim. State your conclusion about H_0.

(d) State your conclusion about the original claim.

Answer 1

(a)        Let x represents the list price.

Let y represents the selling price.

Serial No.	x	y	d = x - y	d2
1	490	485	5	25
2	275	275	0	0
3	289	280	9	81
4	349	360	-11	121
5	460	465	-5	25
6	499	490	9	81
7	325	340	-15	225
8	380	395	-15	225
9	299	315	-16	256
Total	3366	3405	-39	1039

Therefore, the mean of the differences is -4.33.

(b) A group of realtors wants to test the claim that houses are selling for more than the list price.

Let represents the mean difference between the selling price and list price.

The null and the alternative hypothesis can be stated as:

The claim is that . The negation of the claim is '>'.

(c)

The appropriate test statistic to be used is:

                                                                             

The degree of freedom (v) is,

Using t-table and degrees of freedom 8, the p-value is 0.1250.

Since the p-value (0.1250) is smaller than the significance value (0.05), the decision is fail to reject the null hypothesis.

(d):

In conclusion, there is not enough evidence to support the claim; that is, there is a insufficient evidence to claim that houses are selling for more than the list price