STA 210 Chapter 2 Homework

Suppose we construct a histogram of these twelve "Murders" values. We choose the smallest bin to have 420 as a left endpoint and use a bin width of 50. Which of the following has to be the result? Please have a look at page 30 graphs and choose the correct answer. III IV I II

II

One of the 9 people on the bus was a snoozing journalist who woke up just after Mr. Gates got on. She proceeded to do a survey of salaries for the nine riders and reported the average the next day in the paper. Would this create an inaccurate inference regarding the typical income of Seattle residents? Why? Yes. Most residents of Seattle are quite wealthy, and the salaries of the other eight on the bus will pull the mean down. No. Most residents of Seattle will make a lot less than Mr. Gates, so it is quite appropriate that the other eight salaries on the bus pull the reported mean down to a realistic level. Most residents of Seattle will make a lot less than Mr. Gates, so the reported mean will be an exaggeration. No. Most residents of Seattle are quite wealthy, so the mean she is reporting will be right in line with the average in all of Seattle.

Most residents of Seattle will make a lot less than Mr. Gates, so the reported mean will be an exaggeration.

Please read Beyond the numbers , Problem 1 on page 27 , and then answer the question. Question: Is the 50,000 figure right? No. 500000/60 = 833.33, not 34.99. Yes. 50,000/300,000 = 0.1667; and 0.1667/20994 = .3499. Yes. 300000/60 = 50000. No. 300000/60 = 5000, not 50000.

No. 300000/60 = 5000, not 50000.

Versions of the following completely-made-up story have been told elsewhere. Suppose there are exactly 9 people on a bus in Seattle, and the average of their yearly incomes is $65,000. At the next stop, the highest paid person on the bus (with an income of $120,000 per year) gets off, and Bill Gates gets on. Mr. Gates makes 7.6 billion dollars a year. Please answer the next 3 questions using this scenario. Question: What is the new average salary of people on the bus? $844,496,111.10 $844,496.00 $120,000.00 The same as before

$844,496,111.10

Use the table on page 35 in your textbook and answer the following question: What is the coefficient of variation for this group of ten person? 1.29 0.10 0.05 0.61

0.05

Please use the data set on page 36 and answer the following question: What is the coefficient of variation for this group of eleven persons? 0.05 0.61 1.29 0.10

0.10

Assume there are ten possible pairs of days an employee could pick from, and that list of the sets of ten pairs suggested in the question above is the right one. If a pair was just picked at random, what is the chance that they'd pick Monday and Friday as the pair, and does this suggest the secretary (in the amended dialogue) has uncovered a bias? 4 in 10. Yes, if 40% are choosing that pair of days, and there is exactly that chance of randomly choosing that pair of days, then this is clear evidence of bias in the days the employees are choosing. 1 in 10. Yes, if 40% are choosing Monday and Friday, that is evidence of bias toward that pair. 4 in 10. But that is the exactly what the secretary notices was happening, so no evidence of bias. 1 in 10. No evidence of bias since every pair had an equal chance of being chosen.

1 in 10. Yes, if 40% are choosing Monday and Friday, that is evidence of bias toward that pair.

Nursing Knowledge Needed On June 2, 2007, a nurse in Wales accidentally injected an 85-year-old patient with a lethal amount of insulin during a home visit. While the syringes used to inject insulin are typically marked with insulin units instead of the usual milliliters, this nurse found herself without an insulin syringe on hand. So she retrieved a common syringe from her car and proceeded to do the transformation from milliliters to insulin units in her head. If 1 milliliter equals 100 insulin units, how many milliliters should the patient have been given if she had been prescribed 36 units? 1 milliliter = 100 units so 0.01 milliliter = 10 units. It follows that 36 milliliters = 36 units. So she should have injected the patient with 36 milliliters. 1 milliliter = 100 units so 0.1 milliliter = 1 unit. It follows that 0.36 milliliters = 36 units. So she should have injected the patient with 0.36 milliliters. 1 milliliter = 100 units so 0.01 milliliter = 1 unit. It follows that 0.36 milliliters = 3.6 units. So she should have injected the patient with 3.6 milliliters. 1 milliliter = 100 units so 0.01 milliliter = 1 unit. It follows that 0.36 milliliters = 36 units. So she should have injected the patient with 0.36 milliliters.

1 milliliter = 100 units so 0.01 milliliter = 1 unit. It follows that 0.36 milliliters = 36 units. So she should have injected the patient with 0.36 milliliters.

Please read Beyond the Numbers 2, page 29 and answer the question: The "previous school year" being referred to is the 2010-11 year. What was the total number of shootings during the 2010-11 school year? 563 204 319 261

261

Please use the data set on page 36 and answer the following question: What is the median of this data set? 65 70 69.1 67

67

Use the data table on page 35 in your textbook and answer the following question: What is the median wingspan for this group of ten persons? 65 67 70 67.2

67

Winging Out Some Computations Your wingspan is the distance from the tip of the middle finger on your left hand to the tip of the middle finger on your right, with your arms parallel to the ground. The wingspans of 10 hypothetical individuals are recorded in the table page 35 in your textbook. What is the mean wingspan for this group of ten persons? 67 67.2 70 65

67.2

A BIGS Change Suppose the former Kentucky basketball great and subsequent NBA star Anthony Davis drops in for a visit and joins the group of 10 persons in the data set introduced first in the problem above. Please use the data set on page 36 and answer the following question: What is the mean of this new eleven-person data set? 65 67 70 69.1

69.1

Use the data table on page 35 in your textbook and answer the following question: What is the variance for this group of ten persons? 3.05 17.06 9.29 4.13

9.29

A letter to the editor of the New York Times complained about a Times editorial that quoted the following demoralizing statistic:An American woman is beaten by her husband or boyfriend every 15 seconds. The writer of the letter complained: "At that rate, 21 million women would be beaten by their husbands or boyfriends every year. That is simply not the case."Is the letter writer's numerical reasoning correct? Yes. An incident every 15 seconds is 4 per minute, 240 per hour, 5760 per day, 40230 per week, 2096640 per year, about 21 million. No. An incident every 15 seconds is 4 per minute, 240 per hour, 5760 per day, 40230 per week, 209640 per year, not 2096640 per year. Yes. An incident every 15 seconds is 4 per minute, 240 per hour, 5760 per day, 40230 per week, 2096640 per year, about 210.0 million. No. An incident every 15 seconds is 4 per minute, 240 per hour, 5760 per day, 40230 per week, 2096640 per year which is about 2.1 million, not 21 million.

No. An incident every 15 seconds is 4 per minute, 240 per hour, 5760 per day, 40230 per week, 2096640 per year which is about 2.1 million, not 21 million.

Which changed the most, the mean or the median? the median changed the most the mean changed the most neither changed at all they changed the same amount

The mean changed the most

Speaking of violence in Chicago, the table below shows the number of murders in Chicago from 2001 through 2012. Find the mean and the median number of murders over this time period. YEAR2001 20022003200420052006200720082009201020112012Murders667656601453451471448513459436435506 The mean and median are each 2006.5 The mean is 508 and median is 459.5. The mean is 465 and median is 508. The mean is 508 and median is 465.

The mean is 508 and median is 465.

What is the new median salary of people on the bus? $120,000.00 $844,496.00 The same as above $844,496,111.10

The same as above

Difficult Dilbert Dialogue The following dialogue is from a Dilbert cartoon published April 17, 1996.Secretary: Oh my! This is shocking!Boss: What?Secretary: 40% of all sick days taken by our staff are Fridays and Mondays!Boss: What kind of idiot do they think I am?Secretary: Not an idiot savant, they can do math. The secretary is trying to poke fun at her pointy-headed boss. Is she successful or is the joke on her? i. Successful. Assuming an employee picks a single workday at random to be absent, the chances that the employee will pick a Monday or a Friday are 2/5 which is 40% Joke's on her. Assuming an employee picks a single workday at random to be absent, the chances that the employee will pick a Monday or a Friday are 2/5 which is 2.5%, so the author of the cartoon was having his own numeracy issues. Joke's on her. Assuming an employee picks a single workday at random to be absent, the chances that the employee will pick a Monday or a Friday are 2 in 3, not 2 in 5, since once two days are counted, you only have three left. Successful. Assuming an employee picks a single workday at random to be absent, the chances that the employee will pick a Monday or a Friday are (1/2) × (1/2)—since there is a 1 in 2 chance they pick a Monday or they don't—which is 1/4, or about 40%

i. Successful. Assuming an employee picks a single workday at random to be absent, the chances that the employee will pick a Monday or a Friday are 2/5 which is 40%

Let's put some other words into the secretary's dialogue. What if she had said the following?Secretary: When employees choose to take off a pair of sick days in a Tuesday-Monday period of time, 40% of the time they choose Friday and Monday as the two days they pick!The following two questions explore in what sense this is or is not a different situation than the one in the actual cartoon. Question: If we denote the five usual workdays as M,T,W,R, and F (using R for Thursday), which of the following lists all pairs of possible workdays. (M,T), (M,W), (M,R), (M,F), (T,W), (R,M), (T, F), (R,W), (W,F), (R,F) (M,T), (T,W), (W,R), (R,F), (T,M), (W,T), (R,W), (F,R), (M,F), (F,T) (M,F), (T,F), (T,M), (W,M), (W,F), (R,M), (R,F), (F,W), (F,R), (M,R) iii. (M,T), (M,W), (M,R), (M,F), (T,W), (T,R), (T, F), (W,R), (W,F), (R,F)

iii. (M,T), (M,W), (M,R), (M,F), (T,W), (T,R), (T, F), (W,R), (W,F), (R,F)