A community psychologist selects a sample of 16 local police officers to test wh

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 74. She measures their physical endurance on a 100-point physical endurance rating scale. Performance Scores 52 77 60 87 75 95 94 83 81 79 86 61 97 76 91 85 Based on the data given above, compute the one-sample sign test at a 0.05 level of significance. x 74 State whether to retain or reject the null hypothesis. O Retain the null hypothesis. o Reject the null hypothesis

Explanation / Answer

Solution:

The median is 74

Hypothesis : Ho: The physical endurance is equal the median score of 74
Ha: The physical endurance is better that the median score of 74
The table given below:

X = number of + sign = 13

n = number of plus sign = 16

We shall use binomial distribution

with p = 1/2 = 0.5, q = 1/2, n= 16

Test statistic: z = X-np/sqrt(npq)

= 12 - 16(0.5)/sqrt(16(0.5)(0.5))

= 2

Critical value Z at 5% for right tailed test is 1.645

Conclusion:

Since z > Z, We don't accept Ho

Physical endurance is better than the median score of 74

Reject the null hypothesis

Score
difference=Score - 74 52 -22 77 3 60 -14 87 13 75 1 95 21 94 20 83 9 81 7 79 5 86 12 61 -13 97 23 76 2 91 74 85 11

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