Question

A consumer magazine wants to figure out which of two major airlines lost a higher proportion of luggage on international flights. The magazine surveyed Standard Air (population 1) and Down Under airlines (population 2). Standard Air lost 45 out of 600 bags. Down Under airlines lost 30 of 500 bags. Does Standard Air have a higher population proportion of lost bags on international flights? Which of the following is the appropriate conclusion at the 5% significance level?

Answer 1

To Test :-

H0 :- P1 = P2

H1 :- P1 > P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 45 + 30 ) / ( 600 + 500 )
= 0.0682

Z = 0.9827   0.98

Test Criteria :-
Reject null hypothesis if

= 0.9827 < 1.6449, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z > 0.9827 )
P value = 0.8371
Reject null hypothesis if P value <
Since P value = 0.8371 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that Standard Air have a higher population proportion of lost bags on international flights.