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. Once series of tests conducted at Los Angles International Airport (LAX) showed that security guards detected only 73 of the 100 mock weapons carried on by FAA inspectors or included in their carryon 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 is less than the national rate of 0.80 degree i.e., is LAX lax? Test at a 5% significance level using appropriate hypothesis testing procedures. Also determine and interpret the p-value.

Explanation / Answer

Here we want to test that "Is the there sufficient evidence to conclude that the mock weapon detection rate at LAX is less than the national average rate of 0.80"?

So null hypothesis is H0 : P = 0.73

and alternative hypothesis is H1 : P < 0.80

We can used one sample proportion z test.

Let' write given information.

n = sample size = 100

x = number of favourable events = 73

level of significance = 0.05

Using minitab.

The command for one sample proportion z test in minitab is

Stat>>>Basic statistics>>>1-proportion...

Then click on summarized data

number of events = x = 73

Number of trials = n = 100

Click on "Perform hypothesis test

Hypothesized proportion = P = 0.5   (because under the null hypothesis P = 0.5)

then click on option

Level of confidence in percentage = c = ( 1- lpha)*100 = = (1 -0.05)*100 = 95.0

so put "Confidence level " = 95.0

Alternative = less than

then click on "Use test and interval based on normal approximation"

Then click on OK and again click on OK

So we get the following output

MTB > POne 100 73;
SUBC>   Test 0.8;
SUBC>   Alternative -1.

Test and CI for One Proportion

Test of p = 0.8 vs p < 0.8

                                  95% Upper    Exact
Sample   X    N    Sample p      Bound    P-Value
1         73 100   0.730000     0.802075        0.056

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.056 > 0.05 so we used 2nd rule.

That is we failed to reject null hypothesis

Conclusion:

At 5% level of significance there are not sufficient evidence to say that the mock weapon detection rate at LAX is less than the national average rate of 0.80.

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