Respuesta :
The 95% confidence interval for the mean square footage of all the homes in that city = ( 1332.172 , 433.828 )
The mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations), the geometric mean, and the harmonic mean.
Given that,
Sample mean : μ = 883 sqft
Sample standard deviation : σ = 270 sqft
Let s assume,
Sample size n = 1
The population standard deviation is unknown .
The confidence interval for population mean :
μ ± [tex]t_{\frac{a}{2} } \frac{s}{\sqrt{n} }[/tex]
For 95% confidence , significance level = a = 1 - 0.95 = 0.05
Using t-distribution table , Critical t-value = t (a/2, n-1)
= [tex]t_{0.025, 0}[/tex]
= [tex]t_{0.025}[/tex]
= 1.6636, where n-1 is the degree of freedom.
Now , 95% confidence interval for the mean square footage of all the homes in that city will be :-
= 883 ± (1.6636) [tex]\frac{270}{\sqrt{1} }[/tex]
= 883 ± (1.6636 ) 270
= 883 ± 449.172
= ( 883 + 449.172 ) , ( 883 - 449.172 )
= ( 1332.172 , 433.828 )
Therefore,
The 95% confidence interval for the mean square footage of all the homes in that city = ( 1332.172 , 433.828 )
To learn more about Mean and Standard deviation visit :
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