Question

Vail Resorts tracks the proportion of seasonal employees who are rehired each season. Rehiring a seasonal employee is beneficial in many ways, including lowering the costs incurred during the hiring process such as training costs. A random sample of 831 full-time and 400 part-time seasonal employees from 2009 showed that 444 full-time employees were rehired compared with 195 part-time employees.

(a)

Is there a significant difference in the proportion of rehires between the full-time and part-time seasonal employees? (Use α = 0.05.)

(a-1)

Choose the appropriate hypotheses. Assume ππ_F is the proportion of full-time employees and ππ_P is the proportion of part-time employees.

	H0: πF – πP ≥ 0 vs. H1: πF – πP < 0
	H0: πF – πP = 0 vs. H1: πF – πP ≠ 0
	H0: πF – πP ≤ 0 vs. H1: πF – πP > 0

(b)	Find the exact p-value. (Round your answer to 4 decimal places.)

p-value

      

(a-4)

Make a decision.

      

  We (Click to select)do not rejectreject the null hypothesis.

      

(a-5)

Make a decision.

        

  We (Click to select)cancannot conclude that there is a significant difference in the proportion of rehires
  between the full-time and part-time seasonal employees.

Answer 1

(a1)  H0: π_F – π_P = 0 vs. H₁: π_F – π_P ≠ 0

(b)

(a4)  We do not reject the null hypothesis. (because P-value > alpha)

(a5)

We cannot conclude that there is a significant difference in the proportion of rehires   between the full-time and part-time seasonal employees.