Question

A community psychologist selects a sample of 16 local police officers to test whether their physical endurance is better than the median score of 72. She measures their physical endurance on a 100-point physical endurance rating scale.

Performance Scores 79 56 86 87 75 83 89 92 95 90 85 73 76 70 52 64 Based on the data given above, compute the one-sample sign test at a 0.05 level of significance.

x = 0.05

State whether to retain or reject the null hypothesis.

Answer 1

The statistical hypothesis is,

Ho: Median = 72

Ha: Median >72.

The calculation table:

Xi	Xi - 72	Sign
79	7	+
56	-16	-
86	14	+
87	15	+
75	3	+
83	11	+
89	17	+
92	20	+
95	23	+
90	18	+
85	13	+
73	1	+
76	4	+
70	-2	-
52	-20	-
64	-8	-

Total positive sign (s) = 12

Total negative sign (s*) = 4

Total values (n) = s + s* = 12 + 4 = 16

Calculate p-value using Excel function = BINOMDIST(number_success, number_trials, probability_success, TRUE)

=BINOMDIST(12,16,0.5,TRUE)

=0.98936

Since the p-value 0.98936 is greater than the significance level 0.05, so the null hypothes does not rejected.

Hence, the decision is to retain the null hypothesis.