Using 95% Confidence Interval to provide evidence

#1
I am doing this project and have gotten through most of it, but am stuck on the last few questions.

Managers are eager to test a new irrigation system and did so during this year's production cycle of pineapples.

5. How large a sample would you need to take to estimate the mean weight of the pineapples produced within one ounce at a 95% confidence level?
(the sigma is 2.5 ounces in the original problem)

So I did this:

x(bar) +/- z*(sigma/sqrt n)

z*=95%= 1.96
sigma/sqrt n = 1 oz
2.5/sqrt n =1
2.5/sqrt n sqr=1 sqr
2.5 * 2.5/n= 1*2.5=2.5
1.96*2.5=n=4.9

This is not right and I dont know where I went wrong...:confused:

An SRS of 50 pineapples taken from this year's crop had amean weight of 31.6.

6. Use a 95% confidence interval to dertermine whether this sample provides evidence of a change in the mean weight of pineapples produced. Explain your reasoning.


So:

n=50
z*=1.96
mew= 31.6

so do I use the mew +/- z*(sigma/sqrt 50)?
If so, this would be, 31.6 +/- 1.96(sigma/sqrt 50)?


I am so lost at this point....