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Statistics: Flights at O'Hare, FAX costs & Coin Flipping

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22

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. (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 test 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? Flights

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

54

Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more
should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10
or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the .01 level of significance, is the true mean greater than 10? (b) Use Excel to find the right-tail p-value.

56
A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations. (b) Calculate a p-value and interpret it.

62
The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the
same day they are received. If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using α = .025? (See story.news.yahoo.com accessed June 25, 2004.)

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Solution Summary

This solution analyzes different case studies and conducts a hypothesis test by providing the null and alternative hypothesis, calculating and comparing the test statistic to the p-value and making a decision to accept or reject the null hypothesis. All steps and calculations are shown.

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22

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. (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 test 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? Flights

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

Solution:
From the above sample of 30 arrivals the sample mean is calculated as below

Sample Mean (X) = = 200

Given population mean =  = 195 flights per hour

Population Standard Deviation =  = 13 flights

Null Hypothesis H0 :  = 195 ( mean number of arrivals are 195)

Alternative Hypothesis H1 :  > 195 ( mean number of arrivals are greater than 195)

Significance level =  = 0.025

Since the population Standard deviation is known, we use Z-statistic to test our claim.

(a) Decision Rule :

Reject the Null Hypothesis H0 if the p-value of the computed z-statistic is less than our
...

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