Question

calculate the p - value.
an airline claims that the no - show rate for passengers booked on its flights is less than 6%. of 380 randomly selected reservations, 18 were no - shows. determine the p - value for a test of the airlines claim.
0.1499
0.0746
0.1230
0.0600
0.3508

Explanation:

Step1: Calculate sample proportion

The sample proportion \( \hat{p}=\frac{x}{n} \), where \( x = 18 \) (number of no - shows) and \( n=380 \). So, \( \hat{p}=\frac{18}{380}\approx0.0474 \).

Step2: Calculate test statistic

The null hypothesis \( H_{0}:p = 0.06 \) and the alternative hypothesis \( H_{1}:p<0.06 \). The test statistic for a proportion is \( z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}\).
Substitute \( \hat{p}=0.0474\), \(p = 0.06\), and \(n = 380\) into the formula:

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Step3: Find p - value

Since the alternative hypothesis is \( H_{1}:p<0.06 \), the p - value is \(P(Z < z)\). Looking up \(z=-1.03\) in the standard normal table, \(P(Z < - 1.03)=0.1515\approx0.1499\) (due to rounding differences in intermediate steps).

Answer:

0.1499