AP Statistics Chapter 11 Test
Name
Answer the following free response questions to the best of your ability. Please make sure that the grader can
understand your thought process. Please show all work.
1. A grocery store sells four different sizes of a popular brand of corn flakes. For the past few years the
proportion of boxes they sell of each size has been quite stable: 10% Small, 15% Medium, 60% Large, and 15%
Jumbo. They decide to change the pricing of the four sizes and want to see if this changes the proportion of
boxes they sell of each size. To test this, a few weeks after changing the prices they take a simple random
sample of 120 transactions involving corn flakes and count how many boxes of each size were sold. Here are
the results.
(1a) Which chi-square test is appropriate in this setting? Explain your reasoning.
(1b) State the appropriate hypotheses for performing a chi-square test in this setting
(1c) Discuss whether the conditions for this test have been met.
(1d) The chi-square test statistic is 2  9.514. Calculate the P-value (Show all work & Calculator inputs).
(1e) What conclusions can you draw.
Use  = 0.05.
2. Are people born in certain seasons more likely to be allergic to dust mites? Research suggests
this might be true. The table below gives the birth seasons of 400 randomly selected people who
are allergic to dust mites, along with the expected proportion of people born in each season. Do
these data provide convincing evidence that people who suffer from this allergy have a different
birth season distribution?
Birth Season
Winter
Spring
Summer
Fall
Number of allergy
sufferers
107
145
105
133
Proportion of births in
general population
0.30
0.22
0.24
0.24