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 Angles International Airport (LA >) showed that security guards/detected only 73 of the 100 mock weapons carried on by FAA inspectors or included in their carry-on luggage. According to the FAA, "this detection rate was well below the national rate of 80". Is there sufficient evidence to conclude that the mock weapon detection rate at LAX less than the national rate of 0.80? i.e. is LAX lax? Test at a 5% significant level using appropriate hypothesis testing procedures. Also determine and interpret the p-value.

Explanation / Answer

The R code for the given problem:

prop.test(73,100,0.80,alternative="less",conf.level=0.95) / binom.test( )

The R output for the given problem:

  data: 73 and 100
number of successes = 73, number of trials = 100,

test statistic= -1.75 p-value = 0.05583
alternative hypothesis: true probability of success is less than 0.8
95 percent confidence interval:
(0.0000000,0.8020751)
sample estimates:
probability of success
                  0.73                                          

The null hypothesis for the problem is:

H0: mock weapon detection rate at LAX=0.80 VS H1: mock weapon detection rate at LAX<0.80

The test statistic:

z= (p- p0)/ sqrt((p0*(1-p0))/n)

where p: prop. of sucess in the sample

         p0: pre-specified prop (0.80)

         n:sample size

Thus p value from output is 0.055, which means that with alpha=0.05, we see that p value is greater than alpha. This means that we accept H0 and conclude that mock weapon detection rate at LAX=0.80.

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