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 72. She measures their physical endurance on a 100-point physical endurance rating scale. Performance Scores 77 78 52 80 91 76 74 88 83 85 81 73 56 95 82 67 Based on the data given above, compute the one-sample sign test at a 0.05 level of significance. x = State whether to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis.

Explanation / Answer

Sol:

To test the hypothesis that H0: The physical endurance is equal to the median score of 72; H1: The physical endurance better than the median score of 72

Test statistic, z = (S-np)/Sqrt(np(1-p))

Where S = no. of signs greater than the median value of 72

n is the total no. of observations

p = 0.5 (since the distribution is binomial)

put a positive sign for all values greater than the median 72 and a negative sign for those less than 72. Since H1 is to test is endurance > 72, take S as the no. of positive signs.

Here, S = 13, n = 16, p = 0.5

Substituting, Z = 2.5, which is greater than the critical value of 1.96 at 5 % level of significance. Hence, reject Ho and conclude that the physical endurance is better than the median score of 72.

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