Question

Total Value	Heated Area	AC	FP
$147,021	1,138	YES	NO
$174,624	1,224	YES	YES
$213,309	1,456	YES	NO
$252,448	1,461	YES	YES
$444,599	2,729	YES	YES
$172,996	1,178	YES	YES
$181,527	1,251	YES	YES
$118,262	1,142	YES	YES
$300,095	1,799	YES	YES
$292,600	2,478	YES	YES
$212,030	1,776	YES	YES
$444,032	2,933	YES	YES
$238,315	2,531	YES	YES
$195,082	1,516	YES	YES
$367,572	2,817	YES	YES
$737,358	3,910	YES	YES
$276,024	1,687	YES	YES
$343,997	2,460	YES	YES
$204,165	1,437	YES	YES
$91,032	904	YES	YES
$137,514	1,689	NO	NO
$360,554	2,295	YES	YES
$319,038	2,200	YES	YES
$678,314	1,730	YES	YES
$44,811	1,345	NO	NO
$182,836	1,116	YES	NO
$241,832	1,952	YES	YES
$165,907	1,120	YES	NO
$155,325	1,450	YES	NO
$152,683	1,156	YES	YES

5. Calculate 95% and 99% confidence intervals for the Total Value assessed, Heated area, Air Conditioning, and Fireplaces based on your sample data. Show your work by hand in doing these, showing which formula you are using, giving the z_α/2 , standard error and margin of error etc...
6. Explain what each of the confidence intervals tell you concerning the homes in Wake County. Write these explanations out using full sentences!  Example: We are 95% confident that the population mean assessed value of the homes is... etc.

Answer 1

Total Value assessed:

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   29          
't value='   tα/2=   2.0452   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   155315.5338   / √   30   =   28356.607126
margin of error , E=t*SE =   2.0452   *   28356.60713   =   57995.773445
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    261530.07   -   57995.773445   =   203534.293222
Interval Upper Limit = x̅ + E =    261530.07   -   57995.773445   =   319525.840112
95%   confidence interval is (   203534.29   < µ <   319525.84   )

----

Level of Significance ,    α =    0.01          
degree of freedom=   DF=n-1=   29          
't value='   tα/2=   2.7564   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   155315.5338   / √   30   =   28356.607126
margin of error , E=t*SE =   2.7564   *   28356.60713   =   78161.752159
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    261530.07   -   78161.752159   =   183368.314508
Interval Upper Limit = x̅ + E =    261530.07   -   78161.752159   =   339691.818825
99%   confidence interval is (   183368.31   < µ <   339691.82   )

Heated area:

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   29          
't value='   tα/2=   2.0452   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   703.0786   / √   30   =   128.363994
margin of error , E=t*SE =   2.0452   *   128.36399   =   262.533845
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    1796.00   -   262.533845   =   1533.466155
Interval Upper Limit = x̅ + E =    1796.00   -   262.533845   =   2058.533845
95%   confidence interval is (   1533.47   < µ <   2058.53   )

------

Level of Significance ,    α =    0.01          
degree of freedom=   DF=n-1=   29          
't value='   tα/2=   2.7564   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   703.0786   / √   30   =   128.363994
margin of error , E=t*SE =   2.7564   *   128.36399   =   353.820703
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    1796.00   -   353.820703   =   1442.179297
Interval Upper Limit = x̅ + E =    1796.00   -   353.820703   =   2149.820703
99%   confidence interval is (   1442.18   < µ <   2149.82   )

Thanks in advance!

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