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Recently, six single-family homes in Corpus Christi in Texas sold at the following prices (in $1,000s):...

Recently, six single-family homes in Corpus Christi in Texas sold at the following prices (in $1,000s):
545, 460, 722, 512, 652, 602. Find a 95% confidence interval for the mean sale price in Corpus Christi.

Math   Statistics-And-Probability   
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Answer #1

Sample mean = X / n = 582.1667

S = sqrt [ X2 - n 2 / (n-1) ] = 95.9717

95% Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 6- 1 ) = 2.571 (From T table )
582.1667 ± 2.571 * 95.9717/√(6)
Lower Limit = 582.1667 - 2.571 * 95.9717/√(6)
Lower Limit = 481.4342
Upper Limit = 582.1667 + 2.571 * 95.9717/√(6)
Upper Limit = 682.8992
95% Confidence interval is ( 481.4342 , 682.8992 )

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