A realtor would like to create a 95% confidence interval for the average price of a house in Franklin County, Ohio. To accomplish this, she collected a random sample of 529 houses and calculated a sample mean price of $320,128. She knows that the population standard deviation for house prices in Franklin County is $50,324. What is her 95% confidence interval?

So on this case the 95% confidence interval would be given by (315839.52;324416.48)    

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean

population mean (variable of interest)

represent the population standard deviation

n=529 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

  (1)

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 95% confidence interval would be given by (315839.52;324416.48)