Statistics Question I can't get the correct answer

Question

The time until maturity of a certain variety of tomato plant normally distributed with mean µ and standard deviation σ = 2.4 days.  I select a simple random sample of four plants of this variety and measure the time until maturity.  The sample yields sample mean = 65.  If I wanted the amrgin of error for the 95% confidence interval to be ± 1 day, I should select a simple random sample of what size? 

Answer 1

Vivian, this involves reverse engineering the solution.  In your previous problems you had a known sample size and wanted to compute the confidence interval, now you know the interval, and want to compute the sample size.

 

Standard Error of the Mean (SEM) = σ/√n

 

Confidence Interval is 65 ± z • SEM or 65 ± z • σ/√n

 

In this case we want z • σ/√n = 1 day

 

If you multiply both sides of this equation by √n you get

 

z • σ = √n and squaring both sides you get (z • σ)² = n

 

So if you look up the z value for a 95% confidence interval (1.96) multiply it by 2.4 days and then square that number, and round up you'll get your minimum sample size to guarantee a confidence interval of less than 1 day.