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. 187 180 183 212 193 200 185 188 200 206 196 210 217 222 222 183 189 222 214 191 219 191 194 208 188 211 210 229 220 190
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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?

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.

Step-by-step 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.

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints