Question

Recently, six single-family homes San Luis Obispo County in California sold at the following (in $1,000s): 549, 449, 705, 529, 639, 609 A. Construct the 95% confidence interval for the mean sale price in San Luis Obispo County

Answer 1

Let X : sale price of home in San Luis obispo Country

Xbar = sample mean = 580

s = sample standard deviation = 90.188

The 95% confidence interval for the mean sale price in San Luis obispo Country

xbar - t_{​​​​​​a/2}*( s/√n) < < xbar + t_{​​​​​​a/2}*( s/√n)

For confidence level c = 0.95 and degrees of freedom = n -1

Degrees of freedom = 6 - 1 = 5

t_{​​​​​​a/2 , n -1} = t_{​​​​​​0.025, 5} = 2.571

580 - 2.571*(90.189/√6) < < 580 + 2.571*(90.189/√6)

485.337 <   < 674.663

This is 95% confidence interval for the mean sale price in San Luis Obispo County