Question

As part of a real estate companys study, the selling prices of 50 homes in a particular neighborhood were gathered. The sample mean price was $234,000. Assume that the population standard deviation is known to be $28500. Find a 95% confidence interval for the population mean selling price of all homes in this ne ghborhood. State the error bound used in your calculation Which distribution should be used to hnd the confidence interval? The standard normal distribution should be used because the mean is given The Student's distribution should be used because the sample standard deviation is given The Student's t-distribution should be used because the sample mean is larger than 30. The standard normal distribution should be used because the population standard deviation is known.

Answer 1

n = 50

sample mean = 234000

population sd = 28500

95% CI.

Distribution to be used:

The standard normal distribution should be used because the population standard deviation is known.

z value for 95% CI =1.96

$E = z * \frac{\sigma }{\sqrt{n}} = 1.96 *\frac{ 28500}{\sqrt{50}}$

E = 7899.80

CI = mean +/- 7899.80

CI = (226100.20 , 241899.80 )