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

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 16 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 203 flights per hour.

201 220 193 216 187 189 179 215 223 186 174 214 201 203 215 178 205 181 213 183 211 215 205 222 218 179 214 217 223 210

(a) Set up a right-tailed decision rule at = .025 to decide whether there has been a significant increase in the mean number of arrivals per hour. Choose the appropriate hypothesis.

a. H1: > 195, reject H1 if z < 1.960

b. H1: < 195, reject H1 if z > 1.960

c. H0: 195, reject H0 if z < 1.960

d. H0: 195, reject H0 if z > 1.960

(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 = .01?

a. No, z.01 = 2.33 and 2.74 > 2.33, so we would still have concluded that there has been a significant increase in the average number of flight departures.

b. Yes, z.01 = 2.33 and 2.74 > 2.33, so we would still have concluded that there is no evidence to indicate a significant increase.

(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.

Explanation / Answer

a)

ho: u<= 195

h1: u > 195

d. H0: 195, reject H0 if z > 1.960

b-1)

test statistic:

z= (mean-u)/(sd/sqrt(n))

mean 203 AVERAGE(A2:A31)

u 195

sd 16

n= 30

z= (mean-u)/(sd/sqrt(n))

2.74

b-2)

since z > z(a), I reject ho and conclude that u>195

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

b-3)

when a=0.01

z(a)= z(0.01)= 2.33

since z > z(a), I reject ho and conclude that u>195

a. No, z.01 = 2.33 and 2.74 > 2.33, so we would still have concluded that there has been a significant increase in the average number of flight departures.

c)

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

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