You estimated the average rental cost of a 2 bedroom apartment in denton. a random sample of 16 apartments was taken. the sample mean is $800 with a known standard deviation of $160. the error for this calculation, using a 95% ci is $78.40. you decide you cannot have this large an error and want to reduce the error to $60. what size sample should you take? group of answer choices

The new sample size required in order to have the same confidence 95% and reduce the margin of erro to $60 is:

n=28

Step-by-step explanation:

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".  

Assuming the X follows a normal distribution  

And the distribution for is:

We know that the margin of error for a confidence interval is given by:  

  (1)  

The next step would be find the value of , and  

Using the normal standard table, excel or a calculator we see that:  

If we solve for n from formula (1) we got:  

And we have everything to replace into the formula:  

And this value agrees with the sample size given.

For the case of the problem we ar einterested on Me= $60, and we need to find the new sample size required to mantain the confidence level at 95%. We know that n is given by this formula:

And now we can replace the new value of Me and see what we got, like this:

And if we round up the answer we see that the value of n to ensure the margin of error required $ is n=28.