Question

6. Are pedigreed dogs more likely to exhibit neurotic behavior compared to mixed breed dogs? A pet psychologist studied a random sample of 400 dogs consisting of 160 with pedigrees and 240 mixed breed dogs. 56 of the pedigreed dogs and 60 of the mixed breed dogs were judged to be neurotic. Test at 5% significance level whether the proportion of neurotics among pedigreed dogs is significantly higher than the proportion among mixed breed dogs. Show all work and formulas

Answer 1

To Test :-

H0 :- P1 = P2

H1 :- P1 > P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 56 + 60 ) / ( 160 + 240 )
= 0.29


Z = 2.1593

Test Criteria :-
Reject null hypothesis if

= 2.1593 > 1.6449, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( Z > 2.1593 )
P value = 0.0154
Reject null hypothesis if P value <
Since P value = 0.0154 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that the proportion of neurotics among pedigreed dogs is significantly higher than the proportion among mixed breed dogs.