9.1 – 9.2 Review
AP Statistics
Name:
1. For each of the following settings, define the parameter of interest and write the appropriate null and
alternative hypotheses for the test that is described.
(a) The mean weight of loaves of bread produced at the bakery where you work is supposed to be one
pound. You are the supervisor of quality control at the bakery, and you are concerned that new
personnel are producing loaves that have a mean weight of more than one pound.
(b) According to the Humane Society, 33% of households in the United States own at least one cat. You
are interested in determining whether the proportion of households of the students at your school that
own at least one cat is different from the national proportion.
2. Consider the bakery problem in question 1(a). Suppose you weigh an SRS of bread loaves and find that
the mean weight is 1.025 pounds, which yields a P-value of 0.086.
(a) Interpret the P-value in the context of the problem.
(b) What conclusion would you draw at the = 0.05 level? At the = 0.10 level?
3. Eleven percent of the products produced by an industrial process over the past several months have failed
to conform to specifications. The company modifies the process in an attempt to reduce the rate of
nonconformities. In a random sample of 300 items from a trial run, the modified process produces16
nonconforming item. Do these results provide convincing evidence that the modification is effective?
Support your conclusion with a test of significance.
Answers:
1a)
1b)
H o :   1 pound
H a :   1 pound
H o : p  0.33
H a : p  0.33
where  is the mean weight of the loaves of bread produced at the bakery.
where p is the proportion of students at your school who own at least one cat.
2a) If the true mean weight of bread loaves at this bakery is one pound, there is an 8.6% chance of getting a sample of
this size with a mean weight of 1.025 pounds or more.
2b) At the   0.05 level, I will fail to reject H o . There is not significant evidence to suggest that the mean weight of
the loaves of bread is more than one pound.
2b) At the   0.1 level, I will reject H o . There is significant evidence to suggest that the mean weight of the loaves of
bread is more than one pound.
3) We will perform a one-propertion z-test at the   0.05 level.
H o : p  0.11
H a : p  0.11
where p is the proportion of nonconforming products.
We are told this is a random sample. It is reasonable to say there are more than 3000 products produced by this
company.
n  po  300  0.11  33  10 
n  1  po   300  0.89  267  10 
z
p  po
po 1  po 
n

0.053  0.11
 0.11 0.89 
 3.137
300
P  z  3.137   0.00085
z  3.137
Since the p-value is basically zero, I will reject H o . There is significant evidence to suggest that the modified process is
effective at reducing the rate of nonconformities.