Question

Out of 30 randomly sampled black bears, 8 had missing tags. Test the claim that the proportion of black bears missing tags is different from the population proportion of 34%. Use alpha = 0.05

Answer 1

1) Hypothesis:

H₀ : p=0.34

H₁: p 0.34

2) n= 30

The sample proportion = p^{^} = 8/30 = 0.27

(p(1-p)/n) = (0.34*0.66)/30 = 0.0865

Test statistic Z = (p^{^}-p​​​​​)/(p(1-p)/n)

= (0.27-0.34)/0.0865

Test statistic Z = -0.8092

Now calculate p value for Z test statistic is 0.4179.

P value = 0.4179

3) result : do not reject null hypothesis.

4) conclusion:

The p value (0.4179) is greater than 0.05 level of significance that is do not reject null hypothesis at 5% level of significance.