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 14 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 202 flights per hour.

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(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.
(b) Carry out the lest and make the decision. Is it close? Would the decision be different if you used α=.01?
(c) What assumptions are you making, if any?

Answer 1

Part A:

Since the calculated value of z falls in the critical region we conclude that there has been a significant increase in the mean number of arrivals per hour at 0.025 significance level.

Part B:

The calculated value of z =2.73 falls in the critical region we conclude that there has been a significant increase in the mean number of arrivals per hour at 0.01 significance level as well.

Part C:

We are assuming that the standard deviation of the population is equal to the standard deviation of the sample as n= 30 and it is a normal distribution.

Explanation:

The population mean = u= 195

The population standard deviation = σ= 14

The sample mean = x`= 202

The sample standard deviation = s=

Sample size = n= 30

Let the null and alternate hypotheses be

H0: u ≤ 195 against the claim Ha: u > 195

The significance level ∝= 0.025

Calculating z

z= x`-u/σ/√n

z= 202-195/14/√30

Z= 7/14/5.477

z= 7/2.556

z=2.73

Part A:

The critical region for Z∝= 0.025 is Z>1.96 for right tailed test

Since the calculated value of z falls in the critical region we conclude that there has been a significant increase in the mean number of arrivals per hour at 0.025 significance level.

Part B:

The critical region for Z∝= 0.01 is Z > 2.33 for right tailed test

The calculated value of z =2.73 falls in the critical region we conclude that there has been a significant increase in the mean number of arrivals per hour at 0.01 significance level as well.

Part C:

We are assuming that the standard deviation of the population is equal to the standard deviation of the sample as n= 30 and it is a normal distribution.