Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places.
-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. Find the P-value for a test of the airline's claim.
A)0.7939
B)0.2061
C)0.4122
D)0.0206

Question

Quizplus · Accepted Answer

To test the airline's claim that the no-show rate is less than 6%, we first calculate the test statistic using the formula for a proportion test. The observed proportion of no-shows is 18/380 = 0.0474. The null hypothesis is that the no-show rate is 6% (p0 = 0.06). The test statistic (z) is calculated using the formula z = (p - p0) / sqrt(p0(1-p0)/n), where p is the sample proportion, p0 is the null hypothesis proportion, and n is the sample size. Plugging in the values, we get z = (0.0474 - 0.06) / sqrt(0.06*0.94/380) = -1.271. Using a standard normal distribution table or calculator, the P-value for a z-score of -1.271 (for a one-tailed test, since the claim is "less than") is approximately 0.2061. This means there is a 20.61% chance of observing a no-show rate as extreme as 4.74% or more extreme, given that the true no-show rate is 6%.

Find the P-Value for the Indicated Hypothesis Test