Question

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	208	222	221

(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.

1. H₁: μ > 196, reject H₁ if z < 1.96
2. H₁: μ < 196, reject H₁ if z > 1.96
3. H₀: μ ≥ 196, reject H₀ if z < 1.96
4. H₀: μ ≤ 196, reject H₀ if z > 1.96

• 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 been a significant increase in the average number of flight departures.

• There has not 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. Yes, z_.01 = 2.33 and 2.11 < 2.33, so we would still have concluded that there is no evidence to indicate a significant increase.

b. No, z_.01 = 2.33 and 2.11 < 2.33, so we would still have concluded that there has been a significant increase in the average number of flight departures.

• a

• b

(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.

Answer 1

Ans a ) for a right-tailed decision rule

option a is true

H₁: μ > 196, reject H₁ if z < 1.96

b ) since population standard deviation is known so we will use z test

One-Sample Z: data

Test of μ = 195 vs > 195
The assumed standard deviation = 13

Variable N Mean StDev SE Mean 95% Lower Bound Z P
data 30 200.00 13.19 2.37 196.10 2.11 0.018

b-1 ) the test statistic z = 2.11

b-2 ) since 2.11 >1.96 , so reject H0

There has been a significant increase in the average number of flight departures.

b -3 ) at α = .01

a. Yes, z_.01 = 2.33 and 2.11 < 2.33, so we would still have concluded that there is no evidence to indicate a significant increase.
c ) We have assumed a normal population or at least one that is not badly skewed.