In the airline business, "on-time" flight arrival is important for connecting flights and general customer satisfaction. Is there a difference between summer and winter average on-time flight arrivals? Let x1 be a random variable that represents percentage of on-time arrivals at major airports in the summer. Let x2 be a random variable that represents percentage of on-time arrivals at major airports in the winter. A random sample of n1 = 16 major airports showed that x1 = 74.2%, with s1 = 5.1%. A random sample of n2 = 18 major airports showed that x2 = 69.7%, with s2 = 8.5%. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. (a) Does this information indicate a difference (either way) in the population mean percentage of on-time arrivals for summer compared to winter? Use α = 0.05. (i) What is the level of significance? What is the value of the sample test statistic? (Round your answer to three decimal places.) (b) Find a 95% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit % upper limit %
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
In the airline business, "on-time" flight arrival is important for connecting flights and general customer satisfaction. Is there a difference between summer and winter average on-time flight arrivals? Let
be a random variable that represents percentage of on-time arrivals at major airports in the summer. Let
be a random variable that represents percentage of on-time arrivals at major airports in the winter. A random sample of
major airports showed that
with
A random sample of
major airports showed that
with
Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer.
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