Q: 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.


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

The 'the population mean fill differs' implies a two-sided test. With a two sided test, you split the alpha level of 0.01 to 0.005 for both tails of the normal distribution. Use the inverse of Normal distribution to find the z value at 0.005. This is z*. Compare z* and z.

A: The z statistic is obtained by taking the observed value of the test statistic (the sample mean) subtract the assumed population mean and divide by the standard error of the mean.  That gives you the z value.  For this one-sided test compare it to the value for which the cdf of the normal distribution is 0.01.
