At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a
ID: 3060045 • Letter: A
Question
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 6 ml.
(a) The normal distribution should be used for the sample mean because
(You may select more than one 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: 520, H1: = 520, reject if z < 1.96 or z > 1.96
b. H0: 520, H1: = 520, reject if z > 1.96 or z < 1.96
c. H0: = 520, H1: 520, reject if z > 1.96 or z < 1.96
d. H0: =520, H1: 520, reject if z > 1.96 or z < 1.96
(c) If a sample of 16 bottles shows a mean fill of 522 ml, does this contradict the hypothesis that the true mean is 520 ml?
No Yes
Explanation / Answer
a)the population distribution is known to be normal.
b) c. H0: = 520, H1: 520, reject if z > 1.96 or z < 1.96
c)
here test statistic z =(X-mean)/std error =(522-520)/(6/(16)1/2) =2/1.5 =1.33
as test statistic z does not fall into critical region we can not reject null hypothesis
therefore NO this does not contradict the hypothesis that the true mean is 520 ml