At ajax spring water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. the filling process follows a normal distribution with a known process standard deviation of 4 ml.

(a)
the normal distribution should be used for the sample mean because (you may select more than one answer. click the box with a check mark for the correct answer and click to empty the box for the wrong answer.)

the sample population has a large mean.
the population distribution is known to be normal.
the population standard deviation is known.
the standard deviation is very small.
(b)
set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance.

the hypothesis for a two-tailed decision is
a. h0: μ ≠520, h1: μ = 520, reject if z < −1.96 or z > 1.96
b. h0: μ ≠520, h1: μ = 520, reject if z > 1.96 or z < −1.96
c. h0: μ = 520, h1: μ ≠ 520, reject if z > 1.96 or z < −1.96
d. h0: μ =520, h1: μ ≠ 520, reject if z > −1.96 or z < 1.96
(c)
if a sample of 16 bottles shows a mean fill of 515 ml, does this contradict the hypothesis that the true mean is 520 ml?

yes
no