A marketing researcher wants to find a 96% confidence interval for the mean amount those visitors spend per person per day while visiting a theme park. She knows that the population standard deviation is $12. How large a sample should the researcher select so that the estimate will be within $4 of the population mean?

So then the minimum sample to ensure the condition given is n= 38

Step-by-step explanation:

Notation

represent the sample mean for the sample  

population mean (variable of interest)

represent the population standard deviation

n represent the sample size  

ME = 4 the margin of error desired

Solution to the problem

When we create a confidence interval for the mean the margin of error is given by this formula:

   (a)

And on this case we have that ME =4 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

  (b)

The critical value for 96% of confidence interval now can be founded using the normal distribution. The significance is . And in excel we can use this formula to find it:"=-NORM.INV(0.02;0;1)", and we got , replacing into formula (b) we got:

So then the minimum sample to ensure the condition given is n= 38

21

step-by-step explanation: