Question

Barbara Dwyer, the manager at Lux 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, Barbara is especially interested in maintaining consistency in service. Barbara 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). She 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		Late
38	19	111	113
21	50	111	85
41	33	115	119
63	54	118	132
46	42	119	133
48	43	120	121
57	56	121	115
57	63	125	130
80	46	144	126
63	46	140	124
65	51	110	132
57	42	118	111

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.

p-value  0.10

• 0.05  p-value < 0.10
• 0.02  p-value < 0.05
• 0.01  p-value < 0.02

• p-value < 0.01

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

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

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

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

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

d. Interpret the results at  αα = 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

a) H₀: σ₁² / σ₂² = 1, H_A: σ₁² / σ₂² ≠ 1

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b-2) P-value =2F.DIST.RT(1.329,23,23) = 0.50060

      P-value > 0.10

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

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