AP Statistics Mr. Tobar Summer Assignment Chapter 1 Questions. Date

Transcription

1 AP Statistics Name Mr. Tobar Summer Assignment Chapter 1 Questions. Date After reading chapter 1, answer the following questions to the best of your knowledge. 1. This table includes all recent hires at a supermarket chain. Status Hourly Salaried Total Age Under or Older Total a. What percentage of recent hires are younger than 30? b. What percentage of salaried recent hires are younger than 30? c. What percentage of recent hires who were younger than 30 are salaried? d. Does this table support the claim that the supermarket chain is more likely to place a person 30 or older into a salaried position than it is to place a person younger than 30 into a salaried position? Justify your answer.

2 2. These lists show the ages of the employees in a small company and whether they were laid off or retained. Retained: 65, 23, 18, 41, 37, 36 Laid Off: 28, 37, 41, 35, 25, 38, 45 a. Make a dot plot that can be used to compare the ages of those laid off with the ages of those retained. b. Describe how the distribution of those retained differs from those laid off. c. Does your plot in part a show a clear-cut case of possible age discrimination, a possible case, or no case? Explain.

3 2. This display represents hourly workers laid off in Rounds 1 4. The open circles represent hourly workers who were laid off in that round, while the solid dots represent hourly workers who were retained. Which two rounds show the strongest evidence of possible age discrimination against older workers? Explain. 3. Suppose a company lays off workers aged 30, 35, 56, 57, and 63, and retains workers aged 25, 33, 42, 44, and 48. a. Make a dot plot that displays this situation.

4 b. Suppose you use only the information about whether a person is in the protected class (age 40 or older), rather than the exact age. Do you then have evidence for possible age discrimination? Explain. c. This time use only the information about whether a person is age 50 or older. Does the evidence using age 50 provide stronger or weaker support for a case of possible age discrimination than using age 40? Explain. 4. This table shows the ages and lay off status of 75 workers at a manufacturing plant. Choose the statement that best expresses the conclusion that should be drawn from these data. Number of Younger Workers Number of Older Workers Total Laid Off Retained Total A. There might be discrimination against older workers because more older workers were laid off. B. There might be discrimination against older workers because a larger proportion of older workers were laid off. C. There might be discrimination against younger workers because more younger workers were laid off. D. There might be discrimination against younger workers because a larger proportion of younger workers were laid off. E. There is no evidence of discrimination because both older and younger workers were just as likely to be laid off.

5 5. Mountain Electric Company has been accused of discriminating against employees with high blood pressure in its promotional practices. During the past week, of seven employees with systolic pressures of 107, 115, 138, 141, 158, 162, and 173, two workers were bypassed for promotion (162 and 173). a. What is the average systolic pressure of the workers who were bypassed for promotion? b. Describe a simulation for finding the distribution of the average systolic pressure of two workers bypassed for promotion at random. c. Repeat your simulation five times. Display your results in a dot plot. d. This dot plot shows the distribution of average systolic pressure for the two bypassed workers, for 1071 repetitions. Each dot represents 7 points. Use the dot plot to estimate the probability of getting an average blood pressure as large as or larger than that in part a if workers are selected at random for promotion. e. Is the evidence of blood pressure discrimination relatively strong or relatively weak? Justify your conclusion.

6 6. Dog Day Obedience School has been accused of rejecting dogs with long tails. The most recent data show that out of nine dogs considered for the school, two dogs were rejected. This dot plot shows the distribution of average tail length of rejected dogs for a simulation of 52 runs that modeled this situation of randomly selecting two of the nine dogs. The average tail length of the two dogs rejected was 42 cm. Does this dot plot show strong evidence that Dog Day Obedience School should be asked to explain why it rejected dogs with long tails? Choose the best conclusion. A. Yes, it is unlikely to get an average tail length this long or longer by chance alone. B. Yes, they must have discriminated because 42 cm is longer than the average tail length. C. No, it is reasonably likely to get an average tail length this long or longer by chance alone. D. No, 42 cm isn t that much longer than the average tail length. E. Statistics can t be used to answer this question. 7. Refer to the situation described in Question 5: In the past week, seven workers were up for promotion. Five of them, with systolic pressures of 107, 115, 138, 141, and 158, were promoted. Two workers, with systolic pressures of 162 and 173, were bypassed for promotion. a. List all possible pairs of systolic pressure for workers who might have been bypassed for promotion. b. How many pairs give an average systolic pressure the same as or greater than that of the two workers actually bypassed for promotion? c. If a pair of workers is chosen completely at random to be bypassed for promotion, what is the probability that their average blood pressure is as high as or higher than that of the two workers actually bypassed? d. Is the evidence of blood pressure discrimination relatively strong or weak? Justify your conclusion.