Question

In: Statistics and Probability

The mean arrival rate of flights at O'Hare Airport in marginal weather is 195 flights per...

The mean arrival rate of flights at O'Hare Airport in marginal weather is 195 flights per hour with a historical standard deviation of 17 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days of marginal weather, the mean arrival rate is 201 flights per hour.
223 190 214 196 178 184 183 217 215 175
217 222 181 215 213 207 216 193 224 215
220 176 183 188 186 209 219 185 178 208
  Click here for the Excel Data File
(a)

Set up a right-tailed decision rule at α = .025 to decide whether there has been a significant increase in the mean number of arrivals per hour. Choose the appropriate hypothesis.
a. H1: μ > 195, reject H1 if z < 1.960
b. H1: μ < 195, reject H1 if z > 1.960
c. H0: μ ≥ 195, reject H0 if z < 1.960
d. H0: μ ≤ 195, reject H0 if z > 1.960

  • a

  • b

  • c

  • d
(b-1)

Calculate the test statistic. (Round your answer to 2 decimal places.)
  Test statistic   
(b-2) What is the conclusion?

  • There has not been a significant increase in the average number of flight departures.

  • There has been a significant increase in the average number of flight departures.
(b-3) Would the decision have been different if you used α = .01?
a.

No, z.01 = 2.33 and 1.93 < 2.33, so we would still have concluded that there is no evidence to indicate a significant increase.
b.

Yes, z.01 = 2.33 and 1.93 < 2.33, so we would still have concluded that there has been a significant increase in the average number of flight departures.

  • No

  • Yes
(c) What assumptions are you making, if any?

  • We have assumed that the type of distribution does not matter.

  • We have assumed a normal population or at least one that is not badly skewed.

  • We have assumed that the data follow a uniform distribution.

Solutions

Expert Solution

a)

d.H0: μ ≤ 195, reject H0 if z > 1.960

b-1)

test statistic z =1.93

b-2)

There has not been a significant increase in the average number of flight departures

No, z.01 = 2.33 and 1.93 < 2.33, so we would still have concluded that there is no evidence to indicate a significant increase.

We have assumed a normal population or at least one that is not badly

orchestra answered 2 years ago
Next > < Previous

Related Solutions

The mean arrival rate of flights at O'Hare Airport in marginal weather is 195 flights per...
The mean arrival rate of flights at O'Hare Airport in marginal weather is 195 flights per hour with a historical standard deviation of 13 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days of marginal weather, the mean arrival rate is 200 flights per hour. 210 215 200 189 200 213 202 181 197 199 193 209 215 192 179 196 225 199 196 210 199 188 174 176 202 195 195...
The mean number of arrival at an airport during rush hour is 20 planes per hour...
The mean number of arrival at an airport during rush hour is 20 planes per hour while the mean number of departures is 30 planes per hour. Let us suppose that the arrivals and departures can each be described by a respective poisson process. The number of passengers in each arrival or departure has a mean of 100 and a coefficient of variation of 40%. a.) What is the probability that there will be a total of two arrivals and/or...
A major cab company in Chicago has computed its mean fare from O'Hare Airport to the...
A major cab company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be $25.89, with a standard deviation of $3.10. Based on this information, complete the following statements about the distribution of the company's fares from O'Hare Airport to the Drake Hotel. (a) According to Chebyshev's theorem, at least ?56%75%84%89% of the fares lie between 19.69 dollars and 32.09 dollars. (b) According to Chebyshev's theorem, at least 8/9 (about 89%) of the fares...
A major cab company in Chicago has computed its mean fare from O'Hare Airport to the...
A major cab company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be $ 28.99 , with a standard deviation of $ 3.79 . Based on this information, complete the following statements about the distribution of the company's fares from O'Hare Airport to the Drake Hotel. (a) According to Chebyshev's theorem, at least ?56%75%84%89% of the fares lie between 21.41 dollars and 36.57 dollars. (b) According to Chebyshev's theorem, at least ?56%75%84%89% of...
Find each Poisson probability, using a mean arrival rate of 10 arrivals per hour.    (a)...
Find each Poisson probability, using a mean arrival rate of 10 arrivals per hour.    (a) Seven arrivals. (Round your answer to 4 decimal places.)      Poisson probability        (b) Three arrivals. (Round your answer to 4 decimal places.)      Poisson probability        (c) Fewer than five arrivals. (Round your answer to 4 decimal places.)      Poisson probability       (d) At least 11 arrivals. (Round your answer to 4 decimal places.)      Poisson probability   
At Baywatch City Airport 3 passengers per minute arrive on average. Inter-arrival times are exponentially distributed....
At Baywatch City Airport 3 passengers per minute arrive on average. Inter-arrival times are exponentially distributed. Arriving (actually departing) passengers go through a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a checkpoint is in operation, two employees are required. These two employees work simultaneously to check a single passenger. A checkpoint can check an average of 3 passengers per minute, where the time to check a passenger is also exponentially distributed. Why is this an M/M/1,...
3. You receive emails by a Poisson Arrival Process at a rate of 12 emails per...
3. You receive emails by a Poisson Arrival Process at a rate of 12 emails per hour. (a) (6 points) Find the probability that you receive exactly 3 emails between 4:10 PM and 4:20 PM. (b) (6 points) You start checking your email at 10:00 AM. What is the expected time of your first email? (c) (9 points) Given that you receive exactly 10 emails between 4:00 PM and 5:00 PM, what is the (conditional) distribution of the number of...
You own a barbershop with 2 chairs (2 channels). The mean arrival rate is 8 people...
You own a barbershop with 2 chairs (2 channels). The mean arrival rate is 8 people per hour. The mean service rate is 5 units per hour for each chair. Find the following: What is the probability that no one is in the system? (look in the table) What is the average number of people in the system? What is the average time a person waits for service? What is the average time a person is in the system?
Customers arrive at a two pump system at Poisson rate two per hour. An arrival finding...
Customers arrive at a two pump system at Poisson rate two per hour. An arrival finding the system empty is equally likely to enter service with either pump. An arrival finding one customer in the system will enter service with the idle pump. An arrival finding two others in the system will wait in line for the first free pump. An arrival finding three in the system will not enter. Two service times are exponential with rates one per hour...
1.Suppose small aircraft arrive at a certain airport at a rate of 8 per hour. What...
1.Suppose small aircraft arrive at a certain airport at a rate of 8 per hour. What is the probability that at least 13 small aircrafts arrive during a given hour? 2.A particular telephone number is used to receive both voice calls and fax messages. Suppose that 30% of the incoming calls involve fax messages. Consider a sample of 20 incoming calls, what is the probability that at most 6 of the calls involve a fax message.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT