Question

Vending machines on a college campus offer a variety of snacks. Joe, the purchasing manager in charge of the college's contract, believes the demand for each snack type is the same, and therefore, orders equal quantities of each snack type. For the upcoming fiscal year, the manager might have to cut the budget for snacks, and therefore will need to determine if there is evidence that some snack types are in greater demand, proportionally, than others. The number of snacks of each type sold from vending machines on this campus for the last six months is shown in the following table.

Snack Type	Demand
Chips	15
Candy bars	12
Crackers	13

Perform a hypothesis test at the α = 0.10 level of significance to address this question by filling in the blanks below. Type the correct symbols, words, and numbers. Type < for "less than," > for "greater than", = for "equal to", etc. as needed.

1). Define (or Determine, or Specify) the hypotheses ( p₁corresponds to Chips, p₂ corresponds to Candy bars, etc.). Specify your answers as proportions to three decimal places, not percents.

H₀: p₁ = Blank 1, p₂ = Blank 2, p₃ = Blank 3

H₁: At least one proportion is different from its stated value.

2). Calculate the test statistic. Take all calculations toward the answer to three (3) decimal places; enter your answer to two (2) decimal places.

χ² = Blank 4

3). Determine the rejection (or critical) region. Enter your answer to three (3) decimal places.

All χ² > Blank 5

4). Conclusion (in the context of the problem). Enter one of the terms in parentheses for each blank in this section.

Joe will Blank 6 (reject/fail to reject) the null hypothesis. He Blank 7 (can/cannot) conclude that demand for each snack type is the same.

Answer 1