# Calculating if population mean differs from a given value

I have an exam in two days and can't figure this out at all:

In the local cola canning factory, the mean fill of cans is set at 300 milliliters but there is concern that the population mean fill may not in fact be 300ml. Assume that the standard deviation of the amount of cola in a random can is 1. 2 ml. A random sample of 100 cans showed a mean fill of x̄  299. 64 ml.

Is there evidence at the 1% significance level that the population mean fill differs from 300 ml? To answer this question, carry out in detail a z-test but do not use the p-value method.

Calculate the p-value of the test in (i) above and explain why your decision would be the same as that which you reached in (i) if you had been asked to conduct the test in (i) by the p-value method.

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I guess it would be very helpful to show what you've tried already, and where you're stuck. This is one of the most basic tests in statistics, so you were surely given a text book that explains the methods used. –  slhck Aug 7 '12 at 12:19
I think the talk about not using thr "p-value method" is a little silly. Comparing the observed value of the test statistic to the critical value is the same as comparingthe p-value to 0.01 so why make a point about how you do the test? –  Michael Chernick Aug 7 '12 at 12:29

z = (actual_mean-expected_mean)/(standard_deviation/sqrt(count))