Question

Construct a 90% confidence interval for the population average home sale price in Whatcom county. (b) What does the confidence interval mean? (c) How is the confidence interval related to the Central Limit Theorem? (d) What is the difference between a hypothesis test and a confidence interval?

House	Price
1	819500
2	499950
3	569000
4	220000
5	110000
6	499999
7	389900
8	399000
9	650000
10	459000
11	975000
12	749000
13	848000
14	529000
15	325000
16	895000
17	337250
18	489000
19	485000
20	369000
21	2100000
22	509000
23	469900
24	380000
25	260000
26	475000
27	765000
28	675000
29	649000
30	256500

Answer 1

(a) From the given information, size of the sample n= 30, 건 ΣΧ; Sample mean is == = 571900, Sample standard deviation is s= 1-1 (x; -x) = 356463.9, 72 7 Critical value is Tc = txa/2x-1) = 40.0.2.30-1) = 1.699 from t-tables, 356463.9 Margin of error (E) = f(w/2x-1) = 1.699 = 110572.7996. 130 S V? S S 3) 100(1- a)% confidence interval for population mean is 160/2,8-1): =X+:12,2-1) Jn 90% confidence interval for population mean (44) is 356463.9 7.4748 571900-1.699 ,25.4210+2.7154 = (461327.2004, 682472.7996). 130 38 Therefore, 90% confidence interval for the population average home sale price in Whatcom county is 461327.2004 <4682472.7996. (b) With 90% confidence we can conclude that the average home sale price in Whatcom county is between 461327 2004 and 682472.7996. (c) Central Limit Theorem is to know the nature of the sampling distribution of a statistic, where as confidence interval is used to find the range of an unknown parameter with certain confidence. (d)Both are used for decision making regarding an estimate of the unknown population parameter.