Question

the mayor of a small town wants to estimate the average property value for the houses built in the last year. he randomly selects 15 houses and pays an appraiser to determine the value of each house. the mean value of these houses is $183,100 with a standard deviation of $29,200. calculate a 90% confidence interval for the mean value of new houses in this town. assume the conditions are met. (round each bound to the nearest whole number.)

Explanation:

Step1: Identify critical z-value

For 90% confidence, $z^* = 1.645$

Step2: Calculate standard error

$\text{SE} = \frac{\sigma}{\sqrt{n}} = \frac{29200}{\sqrt{15}} \approx 7531.68$

Step3: Compute margin of error

$ME = z^* \times \text{SE} = 1.645 \times 7531.68 \approx 12389.61$

Step4: Find lower confidence bound

$\bar{x} - ME = 183100 - 12389.61 \approx 170710$

Step5: Find upper confidence bound

$\bar{x} + ME = 183100 + 12389.61 \approx 195490$

Answer:

170710 to 195490