When a study was conducted it was found that of the 220 randomly selected flights, 154 were on time, 18 were a National Aviation System Delay, 20 arriving late , 28 were due to weather. Perform a test to see if there is sufficient evidence at αα = 0.01 to see if these differ from the governments statistics.
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!
According to the Bureau of Transportation Statistics, on-time performance by airlines is described as follows:
| Action | % of time |
| On Time | 70 |
| National Aviation System Delay | 8 |
| Aircraft arriving late | 9 |
| Other (weather and other conditions) | 13 |
When a study was conducted it was found that of the 220 randomly selected flights, 154 were on time, 18 were a National Aviation System Delay, 20 arriving late , 28 were due to weather. Perform a test to see if there is sufficient evidence at αα = 0.01 to see if these differ from the governments statistics.
The correct hypotheses are:
- H0:H0: The sample is a good fit to the Bureau of Transportation Statistics.
HA:HA: The sample is not a good fit to the Bureau of Transportation Statistics.(claim) - H0:H0: The sample is not a good fit to the Bureau of Transportation Statistics.
HA:HA: The sample is a good fit to the Bureau of Transportation Statistics.(claim) - H0:H0: The sample and the Bureau of Transportation Statistics are independent.
HA:HA: The sample and the Bureau of Transportation Statistics are dependent.(claim) - H0:H0: The sample and the Bureau of Transportation Statistics are dependent.
HA:HA: The sample and the Bureau of Transportation Statistics are independent.(claim)
The test value is (round to 3 decimal places)
The p-value is (round to 3 decimal places)
The correct decision is to
- reject H0H0
- do not reject H0H0
The final conclusion is
- There is enough evidence to reject the claim.
- There is not enough evidence to reject the claim.
- There is enough evidence to support the claim.
- There is not enough evidence to support the claim.
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