CONDICIONES DE LOS CERTIFICADOS (i) Moneda de emisión: Serán emitidos en pesos

five randomly chosen workers.

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Chapter Summary 23

a. Estimate the probability that if workers were selected by chance alone for layoff , the average age of those laid off would be as large as or larger than the average age of those in the actual layoffs.

b. If the 60-year-old sues for age discrimination, would Eastbanko have some explaining to do?

E21. In E9, you conducted a simulation to estimate the probability that, just by chance, seven or more of the ten hourly workers who were laid off would be age 40 or older. The ages of the fourteen hourly workers were 22, 25, 33, 35, 38, 48, 53, 55, 55, 55, 55, 56, 59, and 64.

a. How many ways can 10 workers be selected from 14 workers for layoff ? b. If there are a total of 10 layoff s, what

numbers of older workers would it have been possible to lay off ?

c. Using your calculator, find the number of ways that you can lay off

i. seven older workers and three younger workers

ii. eight older workers and two younger workers

iii. nine older workers and one younger worker

d. What is the probability that you will get 7 or more workers age 40 or older if you select 10 of the 14 workers completely at random for layoff ?

E22. Refer to your reasoning in E14, where you computed the probability that the three workers laid off in Round 2 would have an average age of 58 or greater. Describe how your reasoning and conclusions would be different if the workers’ ages were 25, 33, 35, 38, 48, 55, 55, 55, 55, and 55, and the three workers chosen for layoff were all age 55. Is the evidence stronger or weaker for Martin in this situation than in E14?

E23. The Society for the Preservation of Wild Gnus held a raffle last week and sold 50 tickets. The two lucky participants whose tickets were drawn received all-day passes to the Wild Gnu Park in Florida. But there was a near riot when the winners were announced—both winning tickets belonged to society president Filbert Newman’s cousins. After some intense questioning by angry ticket holders, it was determined that only 4 of the 50 tickets belonged to Newman’s cousins and the other 46 tickets belonged to people who were not part of his family. Newman’s final comment to the press was “Hey kids, I guess we were just lucky. Deal with it.”

One member of the Gnu Society was taking a statistics class and decided to deal with it by simulating the drawing. He put 50 tickets in a bowl; 4 of the tickets were marked “C” for “cousin” and 46 were marked “N” for “not a cousin.” The statistics student drew two tickets at random and kept track of the number of cousins picked. A er doing this 1000 times, the student found that 844 draws resulted in two N’s, 149 in one N and one C, and only 7 in two C’s.

a. Use the results of the simulation to estimate the probability that, in a fair drawing, both winning tickets would be held by Newman’s cousins.

b. Using the probability you estimated in part a, write a short paragraph that the statistics student can send to other members of the Gnu Society.

c. Is it possible that Newman’s cousins won the prizes by chance alone? Explain. d. Using reasoning like that in E13 and E14,

compute the exact probability that, in a fair drawing, both winning tickets would be held by Newman’s cousins.

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AP1. This plot shows the ages of the part-time and full-time students who receive financial aid at a small college. Which of the following is a conclusion about students at this college that cannot be drawn from the plot alone?

Part-time students who receive financial aid tend to be older than full-time students who receive financial aid. A larger proportion of part-time students than full-time students receive financial aid.

The oldest student receiving financial aid is a full-time student.

No student under age 18 receives financial aid.

More part-time students than full-time students receive financial aid. AP2. This table classifies hourly and salaried

workers as to whether they were laid off . Do the data support a claim that hourly workers are being treated unfairly?

Yes, because most people laid off were hourly workers.

Yes, because a bigger proportion of hourly workers were laid off than salaried workers.

No, because half of hourly workers were laid off and half were not.

No, because more than half of workers were hourly and less than half salaried.

No, because half of hourly workers were laid off, but more than half of salaried workers were laid off.

AP3. This table shows the number of male and female applicants who applied and were either admitted to or rejected from a graduate program. What proportion of admitted applicants were female?

AP4. For the data in AP3, in order to determine if there is evidence to continue investigating whether the graduate admissions process discriminates against females, a study takes a random sample of 25 out of the 70 applicants to be the “admitted” group. The proportion of females in the sample was computed. This process was repeated for a total of 50 random samples and the results are graphed below. What is the best conclusion to draw from this simulation?

The actual proportion of females among those admitted is very near the center of this distribution, so there is no evidence of discrimination.

The actual proportion of females among those admitted is very near the center of this distribution, so there is strong evidence of discrimination in favor of female applicants.

24 Chapter 1 Statistical Reasoning: Investigating a Claim of Discrimination © 2008 Key Curriculum Press

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The actual proportion of females among those admitted is very near the center of this distribution, so there is strong evidence of discrimination against female applicants.

The actual proportion of females among those admitted is quite a bit above the center of this distribution, so there is strong evidence of discrimination in favor of female applicants.

The actual proportion of females among those admitted is quite a bit below the center of this distribution, so there is strong evidence of discrimination against female applicants.

Investigative Tasks

AP5. People with asthma often use an inhaler to help open up their lungs and breathing passages. A pharmaceutical company has come up with a new compound to put in the inhaler that, they believe, will open up the lungs of the user even more than the standard compound tends to do. Ten volunteers with asthma are randomly split into two groups: one group uses the new compound B and the other uses the standard compound A. The measurements listed in Display 1.18 are the increase in lung capacity (in liters) 1 hour after the use of the inhaler.

a. From simply studying the data in the table, do you think compound B does better than compound A in increasing lung capacity?

b. Construct dot plots for compounds A and B. Does it now appear that compound B tends to give larger measurements than compound A? c. Find the average increase in lung capacity for compound A and for compound B. When you compare these means, does it look to you as if compound B is better than compound A at opening up the lungs?

AP6. Refer to AP5. Your task now is to see whether the observed difference in the means of each treatment group reasonably could be attributed to chance alone. a. Place the ten measurements on separate

slips of paper and mix them in a bag. Select five at random to play the role of the A treatment group; the other five play the role of the B treatment group. This time you will use as your summary statistic the difference between the means of each treatment group. Calculate this difference, mean (compound B) − mean (compound A), for your sample. b. The dot plot in Display 1.19 shows

the results of 50 repetitions of this simulation. Compute the difference between the means for the actual data. Locate this difference on the dot plot. How many simulated differences exceed the actual difference? What proportion?

c. In light of this simulation, do you think it is reasonable to attribute the actual difference to chance alone? Explain.

AP Sample Test 25