Question

in a random sample of 50 Lenawee county residents, the mean amount of property tax owed was $ 1,957. Assume that the population standard deviation for the amount of property tax was $256. Construct a 96% confidence interval for the mean amount of property tax paid by Lenawee County residents.

Answer 1

Solution :

Given that,

Sample size = n = 50

Z_$\alpha$/2 = 2.054

Margin of error = E = Z_$\alpha$/2* ($\sigma$ /$\sqrt$n)

= 2.054 * ( 256/ $\sqrt$ 50)

Margin of error = E = 74.36

At 96% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

1957 - 74.36 < $\mu$ < 1957 + 74.36

1882.64 < $\mu$ < 2031.36

(1882.64 , 2031.36)