A microbrewery plans to conduct a study on beer consumption among men between the ages of 29 and 45. A pilot test indicated that men in this age category consume an average of 6 beers per week with a standard deviation of 2.3. Of the microbrewery seeks a 95% confidence level and a precision of 0.5 beers, what size sample should be used in the study

So the answer for this case would be n=82 rounded up to the nearest integer

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 for the sample  

population mean (variable of interest)

s=2.3 represent the sample standard deviation

n represent the sample size  

Solution to the problem

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

  (1)

The margin of error is given by this formula:

   (2)

And on this case we have that ME =0.5 and we are interested in order to find the value of n, if we solve n from equation (2) we got:

  (3)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got , replacing into formula (3) we got:

So the answer for this case would be n=82 rounded up to the nearest integer

x = -2

y = 848

step-by-step explanation:

plug in the numbers