Question

Airlines are concerned about the ages of their airplanes. Forty commercial airplanes randomly selected by the airline from the GLEN aviation company have the ages given below. If the true median age of the airplanes is more than 15 years old, the airline will be forced to update half of their airplanes at a great expense. Conduct the appropriate test using an significant value = 0.01. Does the airline need to update their airplanes? Do not assume normality. 3.2 22.6 23.1 16.9 0.4 6.6 15.5 22.8 26.3 8.1 15.6 17.0 21.3 15.2 18.7 11.5 4.9 5.3 5.8 20.6 23.1 24.7 3.6 12.4 27.3 22.5 3.9 7.0 16.2 24.1 0.1 2.1 7.7 10.5 23.4 0.7 15.8 6.3 16.9 16.8

Answer 1

Here test is about median and normality cannot be assumed to sign test will be used.

Hypotheses are:

Following table shows the ordered data set:

X	Sign
0.1	-
0.4	-
0.7	-
2.1	-
3.2	-
3.6	-
3.9	-
4.9	-
5.3	-
5.8	-
6.3	-
6.6	-
7	-
7.7	-
8.1	-
10.5	-
11.5	-
12.4	-
15.2	+
15.5	+
15.6	+
15.8	+
16.2	+
16.8	+
16.9	+
16.9	+
17	+
18.7	+
20.6	+
21.3	+
22.5	+
22.6	+
22.8	+
23.1	+
23.1	+
23.4	+
24.1	+
24.7	+
26.3	+
27.3	+

Out of 40 data values, 18 are less than 15 and 22 are greater than 15. So we have 18 negative signs and 22 positive signs. So

Since sample size is large so normal approximation can be used. The z-test statistics will be

Test is right tailed so p-value is:

p-value =P(z > -0.47) = 1 - P(z <= -0.47) = 1 - 0.3192 = 0.6808

Since p-value is greater than 0.01 s we fail to reject the null hypothesis. That is we cannot conclude that the airline need to update their airplanes.