Travelocity would like to test if the average roundtrip airfare between New York and London is less than $1,400. A random sample of 30 flights between New York and London was selected and the airfare was recorded. Assume that the standard deviation for the population of airfares between these two cities is $230 and the true population mean for airfare is $1,330. Using α = 0.10, beta equals ________ .
A)0.3483
B)0.2730
C)0.2483
D)0.1655

Question

Quizplus · Accepted Answer

The correct answer is A.The power of a test is the probability of rejecting the null hypothesis when it is false. In this case, the null hypothesis is that the average roundtrip airfare between New York and London is less than $1,400. The alternative hypothesis is that the average roundtrip airfare between New York and London is greater than or equal to $1,400.The power of the test is given by the following formula:```power = 1 - beta```where beta is the probability of failing to reject the null hypothesis when it is false.In this case, we are given that alpha = 0.10 and the true population mean for airfare is $1,330. We can use the following formula to calculate beta:```beta = P(Z < (1400 - 1330) / (230 / sqrt(30)))```where Z is a standard normal random variable.Plugging in the values, we get:```beta = P(Z < 2.33) = 0.9901```Therefore, the power of the test is:```power = 1 - beta = 1 - 0.9901 = 0.0099```This means that the probability of rejecting the null hypothesis when it is false is 0.0099, or 0.99%.

Travelocity Would Like to Test If the Average Roundtrip Airfare