Concerned about train security, the Federal Train Commission (FTC) has begun imp

Question

Concerned about train security, the Federal Train Commission (FTC) has begun imposing sanctions against stations that fail security tests. One series of tests conducted at Detroit’s Michigan Central Station (MCS) showed that security guards detected only 90 of the 120 mock weapons carried on by FTC inspectors or in their luggage. According to the FTC, the detection rate was well below the national average of 75%. Is there sufficient evidence to conclude that the mock weapon detection rate at MCS is less than the national rate of 0.75? Test using a 5% significance level. Be sure to follow appropriate hypothesis testing procedures.

Explanation / Answer

here we will use 1 sample test of proportion .

null hypothesis: p=0.75

alternate hypotheiss:Ha:p<0.75

for p=0.75 ; and n=120 ; std error =(p*(1-p)/n)1/2 =0.0395

sample proportion phat=90/120=0.75

tehrefore test statsitic z =(phat-p)/std error =(0.75-0.75)/0.0395 =0

for above test statistic p vlaue =0.5

s p value is higher than 0.05 level we can not reject null hypothesis

we do not have sufficient evidence to conclude that mock weapon detection rate at MCS is less than the national rate of 0.75

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