The physical fitness score for a population of police office

The physical fitness score for a population of police officers at a local police station is 72, with a standard deviation of 7 on a 100-point physical endurance scale. Suppose the police chief selects a sample of 49 local police officers from this population and records a mean physical fitness rating on this scale equal to 74. He conducts a one-sample z test to determine whether physical endurance increased at a .05 level of significance.
(a) State the value of the test statistic and whether to retain or reject the null hypothesis.
(b) Compute effect size using Cohen\'s d.

Solution

mu = 72 and sigma = 7

Sample size = n - 49

STd error = sigma/rt 49 = 1

Sample mean x bar = 74

H0: x bar = mu

Ha: x bar > mu

Alpha = 0.05

Right tailed test.

x bar - mu =2

Difference / std error = 2

a) Test statistic = z = 2

p value for z = 2 is 0.0228

As p <0.05 reject null hypothesis

There is no statistical evidence to prove that physical endurance incresed.

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b)

Cohen\'s d = (74 - 75) 5 = 0.2.

Gates\' delta = (74 - 75) 7 = 0.142857.

Hedges\' g = (74 - 75) 6.991786 = 0.143025.