Question

The amount of time a plane deviates from its scheduled arrival time is a measure of performance for airports and airlines, where a positive value means the plane arrived late and a negative value means the plane arrived early. Noah Madbury is an aeronautical engineering student who is writing a report on the amount of time planes deviate from their scheduled arrival time. He would like to show in the report whether the mean deviation of planes from their scheduled arrival times are the same at two local airports, Skyhaven and MacArthur. Noah collects a random sample of arrivals at both airports and records the deviation from their scheduled arrival time in minutes. The sample statistics are shown in the table below. Let μ1 be the population mean deviation, in minutes, of arrivals at Skyhaven and μ2 be the population mean deviation, in minutes, of arrivals at MacArthur. Noah is testing the alternative hypothesis Ha:μ1−μ2≠0. He assumes that the population standard deviations of the two groups are not equal, so uses 81 degrees of freedom. If the t-test statistic is t≈1.56, what is the p-value for this hypothesis test?

Probability	0.10	0.05	0.025	0.01	0.005
Degrees of Freedom
80	1.292	1.664	1.990	2.374	2.639
81	1.292	1.664	1.990	2.373	2.638
82	1.292	1.664	1.989	2.373	2.637
83	1.292	1.663	1.989	2.372	2.636
84	1.292	1.663	1.989	2.372	2.636
85	1.292	1.663	1.988	2.371	2.635
86	1.291	1.663	1.988	2.370	2.634
87	1.291	1.663	1.988	2.370	2.634
88	1.291	1.662	1.987	2.369	2.633
89	1.291	1.662	1.987	2.369	2.632
90	1.291	1.662	1.987	2.368	2.632

Select the correct answer below:

A) p-value <0.01

B) 0.01< p-value <0.05

C) 0.05< p-value <0.10

D) p-value >0.10

Answer 1

Solution :

Degrees of freedom = 81

P-value = 2 * P(t ₈₁ > 1.56) = 0.1227

The p-value for this hypothesis test is:

D) p-value >0.10