108k views
2 votes
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 to support the? airline's claim. Round to four decimal places.

A. 0.0746
B. 0.3508
C. 0.1492
D. 0.8508

User Are
by
8.2k points

1 Answer

4 votes

Final answer:

To support the airline's claim of a no-show rate less than 6%, a hypothesis test is performed. The test statistic is calculated from the observed sample proportion, and the p-value is obtained from a standard normal distribution to compare against the significance level. The final answer is the p-value rounded to four decimal places.

Step-by-step explanation:

Finding the P-Value

To find the p-value for the no-show rate, we first set up the hypothesis test. The null hypothesis (H0) is that the no-show rate is at least 6% (p >= 0.06), and the alternative hypothesis (H1) is that the no-show rate is less than 6% (p < 0.06). The number of no-shows observed is 18 out of 380 reservations, leading to a sample proportion (p-hat) of 18/380.

We then calculate the test statistic using the formula for a one-proportion z-test:

z = (p-hat - p) / sqrt(p*(1-p)/n)
where p-hat is the sample proportion, p is the hypothesized proportion (0.06), and n is the sample size (380).

Our test statistic comes to z = (18/380 - 0.06) / sqrt(0.06*(1-0.06)/380). After calculations, we obtain a z-value. We use this z-value to find the p-value from a standard normal distribution table or software that gives the probability of observing a z-value as extreme as or more extreme than the calculated one.

Since this is a left-tailed test, we find the cumulative probability up to our z-value, giving us the p-value. This p-value will denote the probability of observing a proportion as extreme as or more extreme than our sample proportion, given that the null hypothesis is true.

User Thetoast
by
7.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories