At a large company retreat, management orders subs for lunch. They hypothesize that 50 percent of the attendees will choose a turkey sub, 40 percent will choose a ham sub, and 10 percent will choose a vegetarian sub. Before placing the order, they select a random sample of 50 attendees and determine the type of sub they prefer. The management would like to know if there is convincing evidence that the distribution of sub preference differs from 50 percent turkey, 40 percent ham, and 10 percent vegetarian. What are the appropriate hypotheses?
Answer
A
cap h sub 0 : p sub turkey is equal to 25 , p sub ham is equal to 20 , p sub vegetarian is equal to 5 cap h sub A : Not all of the p sub i 's are as stated.
B
cap h sub 0 : p sub turkey is equal to 0 point 5 , p sub ham is equal to 0 point 4 , p sub vegetarian is equal to 0 point 1 cap h sub A : Not all of the p sub i 's are as stated.
C
cap h sub 0 : Not all of the p sub i 's are as stated. cap h sub A : p sub turkey is equal to 25 , p sub ham is equal to 20 , p sub vegetarian is equal to 5
D
cap h sub 0 : Not all of the p sub i 's are as stated. cap h sub A : p sub turkey is equal to 0 point 5 , p sub ham is equal to 0 point 4 , p sub vegetarian is equal to 0 point 1
Explanation
The null hypothesis states the distribution management expects: 50% turkey, 40% ham, and 10% vegetarian. As proportions, these are 0.5, 0.4, and 0.1. The alternative is that the actual distribution differs, meaning not all of the category proportions equal the stated values, so choice B is correct.
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