Question

Mr. Zillow wants to research the prices in a Subdivision near Disney World called World of Homes. The prices of 14 homes in this subdivision are listed below. As a conclusion for his research, with a 90% confidence level, he prepares a report indicating the confidence interval for the mean prices of "World of Homes".    

World of Homes Prices	$225,000	$320,000	$219,000	$199,000	$275,000	$300,000	$215,000
	$210,000	$307,000	$285,000	$317,000	$195,000	$205,000	$286,000

In his report for the mean prices of "World of Homes", he first presents the value of margin of error which is equal to ___ along with the value of degrees of freedom which is equal to ___.

Moreover, Mr. Zillow's report also indicates the mean prices of "World of Homes" with a lower limit of ___ and an upper limit of ___ with a confidence level of 90%.

Round up or down your values to the closest whole numbers.

Fill in the blanks merely by plugging in integer values ONLY.

Please do not use any commas, decimals, or $ sign.

Answer 1

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   48123.0109
Sample Size ,   n =    14
Sample Mean,    x̅ = ΣX/n =    254142.8571

Level of Significance ,    α =    0.1          
degree of freedom=   DF=n-1=   13          
't value='   tα/2=   1.771   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   48123.0109/√14=   12861.4157          
margin of error , E=t*SE =   1.7709   *   12861.4157   =   22776.710
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    254142.86   -   22776.7105   =   231366.1466
Interval Upper Limit = x̅ + E =    254142.86   -   22776.7105   =   276919.5676
90%   confidence interval is (   231366 < µ <   276920 )

In his report for the mean prices of "World of Homes", he first presents the value of margin of error which is equal to __ 22777 _ along with the value of degrees of freedom which is equal to _13__.

Moreover, Mr. Zillow's report also indicates the mean prices of "World of Homes" with a lower limit of _231366__ and an upper limit of _276920__ with a confidence level of 90%.