In a earlier study it was reported that 60% of fish in a pond were infected with fin rot. Efforts
were made to reduce runoff into the pond and another sample was obtained a few years later.
In the later sample, there were 42 fish with fin rot and 38 healthy fish. Test the null
hypothesis that there has been no change in the probability of fin rot against the alternative
that the probability of fin rot has changed. Use 5% level of significance.
were made to reduce runoff into the pond and another sample was obtained a few years later.
In the later sample, there were 42 fish with fin rot and 38 healthy fish. Test the null
hypothesis that there has been no change in the probability of fin rot against the alternative
that the probability of fin rot has changed. Use 5% level of significance.
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Test of Proportion
Use z-test only. You may remember that for large n=80 (>30), if the population proportion is θ, then the value
(p - θ) / √ {θ (1 - θ) / n }
is close to the value of Z.
H0 : θ = 0.60, H1 : θ ≠ 0.60
p = 42/80 = 0.525, under H0, z = (0.525 - 0.60) / √ {0.60 (1 - 0.60) / 80 } = - 1.37
Two-tailed test, P{Z < - 1.37 } = 0.085, P{|Z| < - 1.37 }=2*P{Z < - 1.37 }=0.17 > 0.05; not significant at 5%.
No evidence of change.
Use z-test only. You may remember that for large n=80 (>30), if the population proportion is θ, then the value
(p - θ) / √ {θ (1 - θ) / n }
is close to the value of Z.
H0 : θ = 0.60, H1 : θ ≠ 0.60
p = 42/80 = 0.525, under H0, z = (0.525 - 0.60) / √ {0.60 (1 - 0.60) / 80 } = - 1.37
Two-tailed test, P{Z < - 1.37 } = 0.085, P{|Z| < - 1.37 }=2*P{Z < - 1.37 }=0.17 > 0.05; not significant at 5%.
No evidence of change.