Question

Reid Harper, the manager at Modix Hotel, makes every effort to ensure that customers attempting to make phone reservations do not have to wait too long to speak with a reservation specialist. Since the hotel accepts phone reservations 24 hours a day, Reid is especially interested in maintaining consistency in service. Reid wants to determine if the variance of wait time in the early morning shift (12:00 am – 6:00 am) differs from that in the late morning shift (6:00 am – 12:00 pm). He uses independently drawn samples of wait time for phone reservations for both shifts for the analysis; a portion of the data is shown in the accompanying table. Assume that wait times are normally distributed.

Early Morning Shift	Late Morning Shift
31	105
62	105
34	160
73	122
31	113
44	136
46	115
50	139
67	138
75	134
58	116
41	124
82	119
59	91
44	125
27	126
46	127
67	115
42	109
52	124
45	120
67	118
60	126
43	117

a. Select the hypotheses to test if the variance of wait time in the early morning shift differs from that in the late morning shift.

• H₀: σ₁² / σ₂² = 1, H_A: σ₁² / σ₂² ≠ 1

• H₀: σ₁² / σ₂² ≤ 1, H_A: σ₁² / σ₂² > 1

• H₀: σ₁² / σ₂² ≥ 1, H_A: σ₁² / σ₂² < 1

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

c. At the 10% significance level, what is your conclusion?

• Reject H₀, since the p-value is more than α.

• Reject H₀, since the p-value is less than α.

• Do not reject H₀, since the p-value is less than α.

• Do not reject H₀, since the p-value is more than α.

d. Interpret the results at  α = 0.10.

• The variance of wait time in the early morning shift is greater than that in the late morning shift.

• The variance of wait time in the early morning shift is not greater than that in the late morning shift.

• The variance of wait time in the early morning shift differs from that in the late morning shift.

• The variance of wait time in the early morning shift does not differ from that in the late morning shift.

Answer 1