Concerned about airport and airline security, the Federal Aviation Administratio

Question

Concerned about airport and airline security, the Federal Aviation Administration (FAA) has begun imposing sanctions against airlines that fail security tests. One series of tests conducted at Los Angeles International Airport (LAX) showed that security guards detected only 73 of the 100 weapons carried on by FAA inspectors or included in their carry-on luggage. According to the FAA, "this detection rate was below the national rate of .80." Is there sufficient evidence to conclude that the mock weapon detection rate at LAX is less than the national rate of 0.80? i.e. is LAX lax? Test at a 5% significance level using appropriate hypothesis testing procedures. Also determine interpret the p-value.

Explanation / Answer

here null hypothesis: p>=0.8

alternate hypothesis: p<0.8

n=100

hence std error =(p(1-p)/n)1/2 =0.04

and phat =73/100=0.73

hence test stat z =(X-mean)/std error =(0.73-0.80)/0.04 =1.75

foir abvoe p value for one tailed test =0.0400

which gives probabilty that z value can be that fat provided null hypothesis is true.

as p vlaue is less then 0.05 we reject null hypothesis and conclude that detection rate is less in LAX then national average of 0.8.

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