At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 538 ml. The filling process follows a normal distribution with a known process standard deviation of 5 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
a
b
c
d
(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