A consumer magazine wants to figure out which of two major airlines lost a highe

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?

Reject H0; we can conclude that the proportion of lost luggage is higher for Standard Air than for Down Under airlines.

Reject H0; we cannot conclude that the proportion of lost luggage is higher for Standard Air than for Down Under airlines.

Fail to reject H0; we can conclude that the proportion of lost luggage is higher for Standard Air than for Down Under airlines.

Fail to reject H0; we cannot conclude that the proportion of lost luggage is higher for Standard Air than for Down Under airline

Explanation / Answer

Sol:

H0:p1=p2

H1:p1>p2

p1=proprtion of standard Air

p2=proportion of down under airlines

Alpha=0.05

p1^=x1/n1=45/600

p2^=x2/n2=30/500

p barx1+x2/n1+n2=45+30/600+500=0.0682

Z=0.075-0.06/sqrt(0.0682*(1-0.0682)(1/600+1/500)

Z=0.983

Z c=1.64

Z<Zc

Do not reject Null hypotehsis

There is no sufficient evidence at 5% leve of significance to support the claim

Fail to reject H0; we cannot conclude that the proportion of lost luggage is higher for Standard Air than for Down Under airline

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