Stats Final chapters 1-5

Compute C13,13.

1

Compute C7,5.

21

Compute Compute P10, 4

5040

Compute P6,6.

720

How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890. A sample of 32 cowboys gave the following years of longevity: (a) Make a stem-and-leaf display for these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) (b) Consider the following quote from Baron von Richthofen in his Cattle Raising on the Plains of North America: "Cowboys are to be found among the sons of the best families. The truth is probably that most were not a drunken, gambling lot, quick to draw and fire their pistols." Does the data distribution of longevity lend credence to this quote?

(a) Longevity of Cowboys 4 - 7 5 - 2 7 8 8 6 - 1 6 6 8 8 7 - 0 2 2 3 3 5 6 7 8 - 4 4 4 5 6 6 7 9 9 - 0 1 1 2 3 7 (b) Yes, these cowboys certainly lived long lives, as evidenced by the high frequency of leaves for stems 7, 8, and 9 (i.e., 70-, 80-, and 90-year-olds).

If two events A and B are independent and you know that P(A) = 0.50, what is the value of P(A | B)?

.50

A recent survey of 1010 U.S. adults selected at random showed that 645 consider the occupation of firefighter to have very great prestige. Estimate the probability (to the nearest hundredth) that a U.S. adult selected at random thinks the occupation of firefighter has very great prestige.

.64

In some reports, the mean and coefficient of variation are given. For instance, one report gives the average number of physician visits by males per year. The average reported is 3.4, and the reported coefficient of variation is 1.7%. Use this information to determine the standard deviation of the annual number of visits to physicians made by males. (Round your answer to three decimal places.)

0.058

Compute C2,2.

1

Compute P5,4.

120

There are 10 qualified applicants for 7 trainee positions in a fast-food management program. How many different groups of trainees can be selected?

120

In the least-squares line ŷ = 5 + 2x, what is the marginal change in ŷ for each unit change in x?

2

The University of Montana ski team has seven entrants in a men's downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the seven team entrants achieve first, second, and third places?

210

There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor; position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position. There are 15 candidates qualified for all three of the positions. Determine the number of different ways the positions can be filled by these applicants.

2730

Barbara is a research biologist for Green Carpet Lawns. She is studying the effects of fertilizer type, temperature at time of application, and water treatment after application. She has two fertilizer types, five temperature zones, and three water treatments to test. Determine the number of different lawn plots she needs in order to test each fertilizer type, temperature range, and water treatment configuration.

30

Compute P10,10.

3628800

Find the weighted average of a data set where 20 has a weight of 3, 40 has a weight of 2, and 50 has a weight of 5.

39

A sales representative must visit seven cities. There are direct air connections between each of the cities. Use the multiplication rule of counting to determine the number of different choices the sales representative has for the order in which to visit the cities.

5040

Compute C8,5.

56

During the Computer Daze special promotion, a customer purchasing a computer and printer is given a choice of three free software packages. There are 8 different software packages from which to select. How many different groups of software packages can be selected?

56

In the Cash Now lottery game there are 20 finalists who submitted entry tickets on time. From these 20 tickets, three grand prize winners will be drawn. The first prize is one million dollars, the second prize is one hundred thousand dollars, and the third prize is ten thousand dollars. Determine the total number of different ways in which the winners can be drawn.

6840

One standard for admission to Redfield College is that the student must rank in the upper quartile of his or her graduating high school class. What is the minimal percentile rank of a successful applicant?

75%

At General Hospital, nurses are given performance evaluations to determine eligibility for merit pay raises. The supervisor rates the nurses on a scale of 1 to 10 (10 being the highest rating) for several activities: promptness, record keeping, appearance, and bedside manner with patients. Then an average is determined by giving a weight of 1 for promptness, 3 for record keeping, 4 for appearance, and 2 for bedside manner with patients. What is the average rating for a nurse with ratings of 6 for promptness, 6 for record keeping, 9 for appearance, and 10 for bedside manner?

8

What is the difference between a parameter and a statistic?

A parameter is a numerical measurement describing data from a population. A statistic is a numerical measurement describing data from a sample.

Your friend is thinking about buying shares of stock in a company. You have been tracking the closing prices of the stock shares for the past 90 trading days. Which type of graph for the data, histogram or time-series, would be best to show your friend? Why?

A time-series graph because the pattern of stock prices over time is more relevant than the frequency of a range of closing prices.

(a) In the least-squares line ŷ = 5 − 9x, what is the value of the slope? (b) When x changes by 1 unit, by how much does ŷ change?

A- -9 B- when x increases by 1 unit, y decreases by 9 units

Given P(A) = 0.6 and P(B) = 0.2, do the following. (a) If A and B are independent events, compute P(A and B). (b) If P(A | B) = 0.3, compute P(A and B).

A- .12 B- .06

M&M plain candies come in various colors. According to the M&M/Mars Department of Consumer Affairs, the distribution of colors for plain M&M candies is as follows. Suppose you have a large bag of plain M&M candies and you choose one candy at random. (a) Find P(green candy or blue candy). Are these outcomes mutually exclusive? Why? (b) Find P (yellow candy or red candy) (c) Find P(not purple candy).

A- .17 Yes choosing a green and blue M&M is not possible B- .38 C- .82

Given P(A) = 0.4, P(B) = 0.7, P(A | B) = 0.3, do the following. (a) Compute P(A and B) (b) Compute P(A or B)

A- .21 b- .89

John runs a computer software store. Yesterday he counted 139 people who walked by the store, 58 of whom came into the store. Of the 58, only 29 bought something in the store. (a) Estimate the probability that a person who walks by the store will enter the store. (b) Estimate the probability that a person who walks into the store will buy something. (c) Estimate the probability that a person who walks by the store will come in and buy something. (d) Estimate the probability that a person who comes into the store will buy nothing.

A- .42 B- .50 C- .21 D- .50

A national park is famous for its beautiful desert landscape and its many natural rock formations. The following table is based on information gathered by a park ranger of all rock formations of at least 3 feet. The height of the rock formation is rounded to the nearest foot. For a rock formation chosen at random from this park, use the preceding information to estimate the probability that the height of the rock formation is as follows. (a) 3 to 9 feet (b) 30 feet or taller (c) 3 to 49 feet (d) 10 to 74 feet (e) 75 feet or taller

A- .44 B- .26 C- .83 D- .52 E- .04

A botanist has developed a new hybrid cotton plant that can withstand insects better than other cotton plants. However, there is some concern about the germination of seeds from the new plant. To estimate the probability that a seed from the new plant will germinate, a random sample of 3000 seeds was planted in warm, moist soil. Of these seeds, 2150 germinated. (a) Use relative frequencies to estimate the probability that a seed will germinate. What is your estimate? (b) Use relative frequencies to estimate the probability that a seed will not germinate. What is your estimate? (c) Either a seed germinates or it does not. What is the sample space in this problem? (d) Do the probabilities assigned to the sample space add up to 1? Should they add up to 1? Explain. (e) Are the outcomes in the sample space of part (c) equally likely?

A- .717 B- .283 C- germinate or not germinate D- Yes, because they cover the entire sample space E- no

Given P(A) = 0.3 and P(B) = 0.5, do the following. (a) If A and B are mutually exclusive events, compute P(A or B). (b) If P(A and B) = 0.2, compute P(A or B).

A- .80 B- .60

Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication. (a) Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (b) Do the probabilities add up to 1? Why should they? What is the sample space in this problem?

A- 0 1 2 3 4 .11 .17 .31 .33 .08 B- Yes, because they cover the entire sample space. 0, 1, 2, 3, 4 personality preferences in common

What is the probability of the following. a) An event A that is certain to occur? b) An event B that is impossible?

A- 1 B-0

a) If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely? (b) Assign probabilities to the outcomes of the sample space of part (a). Do the probabilities add up to 1? Should they add up to 1? Explain. (c) What is the probability of getting a number less than 6 on a single throw? (d) What is the probability of getting 1 or 2 on a single throw?

A- 1, 2, 3, 4, 5, 6; equally likely B- Outcome Probability 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6 Yes, because these values cover the entire sample space. C- 5/6 D- 2/6

You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 7? (b) What is the probability of getting a sum of 11? (c) What is the probability of getting a sum of 7 or 11? Are these outcomes mutually exclusive?

A- 1/6 B- 1/18 C- 2/9 Yes

You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 7? (b) What is the probability of getting a sum of 11? (c) What is the probability of getting a sum of 7 or 11? (Are these outcomes mutually exclusive?

A- 1/6 B- 1/18 C- 4/18 Yes

Consider two data sets. Set A: n = 5; x = 10 Set B: n = 50; x = 10 (a) Suppose the number 11 is included as an additional data value in Set A. Compute x for the new data set. Hint: x = nx. To compute x for the new data set, add 11 to x of the original data set and divide by 6. (b) Suppose the number 11 is included as an additional data value in Set B. Compute x for the new data set. (c) Why does the addition of the number 11 to each data set change the mean for Set A more than it does for Set B?

A- 10.17 B- 10.02 C- Set B has a larger number of data values than set A, so to find the mean of B we divide the sum of the values by a larger value than for A.

Diagnostic tests of medical conditions can have several types of results. The test result can be positive or negative, whether or not a patient has the condition. A positive test (+) indicates that the patient has the condition. A negative test (−) indicates that the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work may be required. Consider a random sample of 200 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for a condition are shown. Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. (a) P(+ | condition present); this is known as the sensitivity of a test. (b) P(− | condition present); this is known as the false-negative rate. (c) P(− | condition absent); this is known as the specificity of a test. (d) P(+ | condition absent); this is known as the false-positive rate. (e) P(condition present and +); this is the predictive value of the test. (f) P(condition present and −).

A- 101/118 B- 17/118 C- 53/82 D- 29/82 E- 101/200 F- 17/200

Certain kinds of tumors tend to recur. The following data represent the lengths of time, in months, for a tumor to recur after chemotherapy For this problem, use five classes. (a) Find the class width. (b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Give relative frequencies to 2 decimal places.) (c) Categorize the basic distribution shape.

A- 12 B- Class Limits: 1 − 12 13 − 24 25 − 36 37 − 48 49 − 60 Class Boundaries: 0.5 − 12.5 12.5 − 24.5 24.5 − 36.5 36.5 − 48.5 48.5 − 60.5 Midpoint 6.5 18.5 30.5 42.5 54.5 Frequency 6 10 5 13 8 Relative Frequency: 0.14 0.24 0.12 0.31 0.19 Cumulative Frequency: 6 16 21 34 42 C- Bimodal

Given the sample data. x:23 19 15 30 25 (a) Find the range. (b) Verify that Σx = 112 and Σx2 = 2,640. (c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s2 and sample standard deviation s. (d) Use the defining formulas to compute the sample variance s2 and sample standard deviation s. (Round your answers to two decimal places.) (e) Suppose the given data comprise the entire population of all x values. Compute the population variance 𝜎2 and population standard deviation 𝜎. (Round your answers to two decimal places.)

A- 15 B- Σx = 112 Σx2 = 2640 C- s2 = 32.8 s = 5.727 D- s2 = 32.8 s = 5.727 E- 𝜎2 = 26.24 𝜎 = 5.12

Given the sample data. x:21 19 13 32 25 (a) Find the range. (b) Verify that Σx = 110 and Σx2 = 2,620. (c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s2 and sample standard deviation s. (d) Use the defining formulas to compute the sample variance s2 and sample standard deviation s. (e) Suppose the given data comprise the entire population of all x values. Compute the population variance 𝜎2 and population standard deviation 𝜎.

A- 19 B- Σx = 110 Σx2 = 2620 C- s2 = 50 s = 7.07 D- s2 = 50 s = 7.07 E- 𝜎2 = 40 𝜎 = 6.32

(a) How many outcomes contain a head and a number greater than 4? (b) Assuming the outcomes displayed in the tree diagram are all equally likely, what is the probability that you will get a head and a number greater than 4 when you flip a coin and toss a die?

A- 2 B- .167

(a) How many outcomes contain a head and a number greater than 4? (b) Probability extension: Assuming the outcomes displayed in the tree diagram are all equally likely, what is the probability that you will get a head and a number greater than 4 when you flip a coin and toss a die?

A- 2 B- .167

In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set. 12, 10, 16, 14, 16 (a) Use the defining formula, the computation formula, or a calculator to compute s. (b) Add 3 to each data value to get the new data set 15, 13, 19, 17, 19. Compute s. (c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?

A- 2.6077 B- 2.6077 C- Adding the same constant c to each data value results in the standard deviation remaining the same.

Consider sample data with x = 25 and s = 5. (a) Compute the coefficient of variation. (b) Compute a 75% Chebyshev interval around the sample mean

A- 20% B- lower limit- 15 upper limit- 35

One professor grades homework by randomly choosing 5 out of 10 homework problems to grade. (a) How many different groups of 5 problems can be chosen from the 10 problems? (b) Probability extension: Jerry did only 5 problems of one assignment. What is the probability that the problems he did comprised the group that was selected to be graded? (c) Silvia did 7 problems. How many different groups of 5 did she complete? groupsWhat is the probability that one of the groups of 5 she completed comprised the group selected to be graded?

A- 252 B- .0040 C- 21 D- .0833

One professor grades homework by randomly choosing 5 out of 10 homework problems to grade. (a) How many different groups of 5 problems can be chosen from the 10 problems? (b) Silvia did 7 problems. How many different groups of 5 did she complete?

A- 252 groups B- 21 groups

Are customers more loyal in the East or in the West? The following table is based on information from a recent study. The columns represent length of customer loyalty (in years) at a primary supermarket. The rows represent regions of the United States. What is the probability that a customer chosen at random has the following characteristics? (a) has been loyal 10 to 14 years (b) has been loyal 10 to 14 years, given that he or she is from the East (c) has been loyal at least 10 years (d) has been loyal at least 10 years, given that he or she is from the West (e) is from the West, given that he or she has been loyal less than 1 year (f) is from the South, given that he or she has been loyal less than 1 year (g) has been loyal 1 or more years, given that he or she is from the East (h) has been loyal 1 or more years, given that he or she is from the West (i) Are the events "from the East" and "loyal 15 or more years" independent? Explain.

A- 291/2113 B- 77/459 C- 902/2113 D- 150/412 E- 41/157 F- 53/157 G- 427/459 H- 371/412 I- No. P(loyal 15 or more years) ≠ P(loyal 15 or more years | East).

(A) How many sequences contain exactly two heads? (b) Probability extension: Assuming the sequences are all equally likely, what is the probability that you will get exactly two heads when you toss a coin three times?

A- 3 B- .375

(a) How many sequences contain exactly 2 heads. (b) Assuming the sequences are all equally likely, what is the probability that you will get exactly two heads when you toss a coin three times?

A- 3 B- .375

You toss a pair of dice. (a) Determine the number of possible pairs of outcomes. (Recall that there are six possible outcomes for each die.) (b) There are three even numbers on each die. How many outcomes are possible with even numbers appearing on each die? (c) Probability extension: What is the probability that both dice will show an even number?

A- 36 B- 9 C- .25

Consider a data set with at least three data values. Suppose the highest value is increased by 10 and the lowest is decreased by 10. (a) Does the mean change? Explain. (b) Does the median change? Explain. (c) Is it possible for the mode to change? Explain.

A- No, the sum of the data does not change. B- No, changing the extreme data values does not affect the median. C- Yes, depending on which data value occurs most frequently after the data are changed

Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on below are based on random samples of size 30, 50, and 100 from the same population. (A) Based on the completed table, select the most reasonable estimate of the range of the population data (B) Does the bulk of the data seem to be between 5 and 9 in all three histograms? (C) The population distribution from which the samples were drawn is symmetric and mound-shaped, with the top of the mound at 7, 95% of the data between 5 and 9, and 99.7% of the data between 4 and 10. How well does each histogram reflect these characteristics?

A- 4 to 10 B- Since there are very few values outside the range 5 to 9, we can say that the bulk of the data is between 5 and 9. C- The three histograms are mound-shaped and the data gradually reduces on either side of the mound in a symmetrical fashion. The highest bar in histogram (i) is at a value of x of 7 units. The highest bar in histogram (ii) is at a value of x of 7 units. The highest bar in histogram (iii) is at a value of x of 6.5 units. So, the average top of the mound can be said to be at a value of x of approximately 7 units. In histogram (i), 96.67 % of the sample data is between 5 and 9 inclusive, and 100 % of the sample data is between 4 and 10 inclusive. In histogram (ii), 94 % of the sample data is between 5 and 9 inclusive, and 100 % of the sample data is between 4 and 10 inclusive. In histogram (iii), 98 % of the sample data is between 5 and 9 inclusive, and 100 % of the sample data is between 4 and 10 inclusive. So, it is reasonable to say that 99.7% of population distribution data is between 4 and 10. Finally, the bulk of the sample data is between 5 and 9. So, it is reasonable to say that 95% of the population distribution data is between 5 and 9.

Consider population data with 𝜇 = 40 and 𝜎 = 2. (a) Compute the coefficient of variation. (b) Compute an 88.9% Chebyshev interval around the population mean.

A- 5% B- lower limit- 34 upper limit- 46

You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 6? (b) What is the probability of getting a sum of 10? (c) What is the probability of getting a sum of 6 or 10? Are these outcomes mutually exclusive?

A- 5/36 B- 1/12 C- 2/9 yes

You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of 6? (b) What is the probability of getting a sum of 10? (c) What is the probability of getting a sum of 6 or 10? Are these outcomes mutually exclusive?

A- 5/36 B- 3/36 C- 8/36 Yes

A recent study gave the information shown in the table about ages of children receiving toys. The percentages represent all toys sold. What is the probability that a toy is purchased for someone in the following age ranges? (a) 6 years old or older (b) 12 years old or younger (c) between 6 and 12 years old (d) between 3 and 9 years old A child between 10 and 12 years old looks at this probability distribution and asks, "Why are people more likely to buy toys for kids older than I am (13 and over) than for kids in my age group (10-12)?" How would you respond?

A- 61% B- 75% C- 36% D- 47% The 13-and-older category may include children up to 17 or 18 years old. This is a larger category.

Where does all the water go? According to the Environmental Protection Agency (EPA), in a typical wetland environment, 37% of the water is outflow; 46% is seepage; 5% evaporates; and 12% remains as water volume in the ecosystem (Reference: United States Environmental Protection Agency Case Studies Report 832-R-93-005). Chloride compounds as residuals from residential areas are a problem for wetlands. Suppose that in a particular wetland environment the following concentrations (mg/l) of chloride compounds were found: outflow, 50.2; seepage, 76.0; remaining due to evaporation, 46.8; in the water volume, 57.0. (a) Compute the weighted average of chlorine compound concentration (mg/l) for this ecological system. (b) Suppose the EPA has established an average chlorine compound concentration target of no more than 58 mg/l. Does this wetlands system meet the target standard for chlorine compound concentration?

A- 62.7 B- No. The average chlorine compound concentration (mg/l) is too high.

Consider the data set. 2, 3, 4, 5, 9 (a) Find the range. (b) Use the defining formula to compute the sample standard deviation s. (Round your answer to two decimal places.) (c) Use the defining formula to compute the population standard deviation 𝜎. (Round your answer to two decimal places.)

A- 7 B- 2.7 C- 2.42

A data set with whole numbers has a low value of 20 and a high value of 82. (a) Find the class width for a frequency table with seven classes. (b) Find the class limits for a frequency table with seven classes.

A- 9 B- First class 20 − 28 Second class 29 − 37 Third class 38 − 46 Fourth class 47 − 55 Fifth class 56 − 64 Sixth class 65 − 73 Seventh class 74 − 82

Angela took a general aptitude test and scored in the 93rd percentile for aptitude in accounting. (a) What percentage of the scores were at or below her score? (b) What percentage were above?

A- 93 B- 7

You are manager of a specialty coffee shop and collect data throughout a full day regarding waiting time for customers from the time they enter the shop until the time they pick up their order. (a) What type of distribution do you think would be most desirable for the waiting times: skewed right, skewed left, mound-shaped symmetric? Explain. (b) What if the distribution for waiting times were bimodal? What might be some explanations?

A- A skewed right distribution would be the most desirable because this would mean there are a lot of short waiting times and only a few long waiting times. B- A bimodal distribution for waiting times might exist if orders are filled at different rates during busy and slow periods.

Consider a series of events. (a) How does a tree diagram help you list all the possible outcomes of a series of events? (b) How can you use a tree diagram to determine the total number of outcomes of a series of events?

A- All possible outcomes are shown as distinct paths from the beginning of the diagram to the end of each last branch. B- Counting the number of final branches gives the total number of outcomes.

a) What is the law of large numbers? b) If you were using the relative frequency of an event to estimate the probability of the event, would it be better to use 100 trials or 500 trials? Explain.

A- As the sample size increases, the relative frequency of outcomes gets closer to the theoretical probability of the outcome. B- It would be better to use 500 trials, because the law of large numbers would take effect.

(a) The video shows many statistics in which Douglas County is higher than most communities in the United States. What is the one area in which the statistics presented suggest that Douglas County is actually lower than many other communities? (b) Which is the most likely used method to compute the average commute time to work in Douglas County? (c) The video lists the major employers in Douglas County, but does not list any statistics with these names. Which of the following statistics would help you understand why they describe these companies as major employers in Douglas County?

A- Diversity B- Researchers collected a random sample of people in Douglas County who are employed and asked them for their commute time. They added up all of these commute times and then divided this number by the number of people in the sample. C- The percentages of employed Douglas County residents who work for each of these companies.

An annual marathon covers a route that has a distance of approximately 26 miles. Winning times for this marathon are all over 2 hours. The following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. (a) Make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. Use two lines per stem. (b) Make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. Use two lines per stem (c) Compare the two distributions. How many times under 15 minutes are in each distribution?

A- Earlier Period 0- NONE 0- 8 9 1- 0 2 2 3 3 1- 5 5 5 6 7 8 8 9 9 2- 0 2 3 3 2- NONE B- Recent Period 0- NONE 0- 7 7 7 7 8 8 8 8 8 9 9 9 9 9 9 1- 0 0 1 4 4 1- NONE C- Earlier period- 7 times Recent period- 20 times

Consider the mode, median, and mean. (a) Which average represents the middle value of a data distribution? (b) Which average represents the most frequent value of a data distribution? (c) Which average takes all the specific values into account?

A- Median B- Mode C- Mean

(a) The video indicates that almost all of the heroin in the United States comes from which two countries? (b) This video uses graphics to depict both qualitative (categorical) and quantitative (numerical) aspects of the heroin trade. Which of the following graphics from the video is an example that depicts one of the qualitative aspects? (c) This video presents a bar graph that compares heroin in pure form to heroin with fentanyl added. What did this graph depict and why was this graph shown?

A- Mexico and Colombia B- The pictures of different ways heroin is smuggled into the United States. C- Seeing the difference in the heights of the two bars helps viewers to better comprehend the large difference in potency between pure heroin and heroin with fentanyl added.

(a) Consider a completely randomized experiment in which a control group is given a placebo for congestion relief and a treatment group is given a new drug for congestion relief. Describe a double-blind procedure for this experiment. (b) What are some benefits of such a procedure? (Select all that apply.)

A- Neither the patients nor those administering the treatments know which patients received which treatments. B- This process should eliminate potential bias from patient psychology regarding benefits of the drug. This process should eliminate potential bias from the treatment administrators.

How would you use a completely randomized experiment in each of the following settings? Is a placebo being used or not? Be specific and give details. (a) A veterinarian wants to test a strain of antibiotic on calves to determine their resistance to common infection. In a pasture are 22 newborn calves. There is enough vaccine for 10 calves. However, blood tests to determine resistance to infection can be done on all calves. (Select all that apply.) (b) The Denver Police Department wants to improve its image with teenagers. A uniformed officer is sent to a school 1 day a week for 10 weeks. Each day the officer visits with students, eats lunch with students, attends pep rallies, and so on. There are 18 schools, but the police department can visit only half of these schools this semester. A survey regarding how teenagers view police is sent to all 18 schools at the end of the semester. (Select all that apply.) (c) A skin patch contains a new drug to help people quit smoking. A group of 75 cigarette smokers have volunteered as subjects to test the new skin patch. For one month, 40 of the volunteers receive skin patches with the new drug. The other volunteers receive skin patches with no drugs. At the end of the two months, each subject is surveyed regarding his or her current smoking habits. (Select all that apply.)

A- No placebo is being used Use random selection to pick 10 calves to inoculate. After inoculation, test all calves to see if there is a difference in resistance to infection between the two groups. B- Use random selection to pick nine schools to visit. After the police visits, survey all the schools to see if there is a difference in views between the two groups. No placebo is being used. C- A placebo patch is used for the remaining 35 volunteers in the second group. Use random selection to pick 40 volunteers for the skin patch with the drug. Then record the smoking habits of all volunteers to see if a difference exists between the two groups.

The New York Times did a special report on polling that was carried in papers across the nation. The article pointed out how readily the results of a survey can be manipulated. Some features that can influence the results of a poll include the following: the number of possible responses, the phrasing of the question, the sampling techniques used (voluntary response or sample designed to be representative), the fact that words may mean different things to different people, the questions that precede the question of interest, and finally, the fact that respondents can offer opinions on issues they know nothing about. (a) Consider the expression "over the last few years." Do you think that this expression means the same time span to everyone? (b) What would be a more precise phrase?

A- No, it could mean 2 years, 3 years, 7 years, etc. B- "Over the past 5 years"

One indicator of an outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80. (a) If a data set has mean 70 and standard deviation 5, is 80 a suspect outlier? (b) If a data set has mean 70 and standard deviation 3, is 80 a suspect outlier?

A- No, since 80 is less than 2.5 standard deviations above the mean. B- Yes, since 80 is more than 2.5 standard deviations above the mean.

Zane is examining two studies involving how different generations classify specified items as either luxuries or necessities. In the first study, generation A is defined to be people ages 14-25. The second study defined generation A to be people ages 18-29. Zane notices that the first study was conducted in 2006 while the second one was conducted in 2010. (a) Are the two studies inconsistent in their description of generation A? (b) According to the 2006 study, what are the birth years of generation A?

A- No, the age ranges updated with the studies. B- 1981 - 1992

Numbers are often assigned to data that are categorical in nature. (a) Consider these number assignments for category items describing electronic ways of expressing personal opinions.1 = Twitter; 2 = e-mail; 3 = text message; 4 = Facebook; 5 = blog Are these numerical assignments at the ordinal data level or higher? Explain. (b) Consider these number assignments for category items describing usefulness of customer service. 1 = not helpful; 2 = somewhat helpful; 3 = very helpful; 4 = extremely helpful Are these numerical assignments at the ordinal data level? Explain. (c) What about at the interval level or higher? Explain.

A- No, they are at the nominal level as there is no apparent ordering in the responses. B-Yes, the data has an ordering to its categories. C- No, while the data has an ordering, and the data can be compared to each other, the differences don't mean anything.

Suppose two events A and B are mutually exclusive, with P(A) ≠ 0 and P(B) ≠ 0. By working through the following steps, you'll see why two mutually exclusive events are not independent. (a) For mutually exclusive events, can event A occur if event B has occurred? What is the value of P(A|B)? (b) Using the information from part (a), can you conclude that events A and B are not independent if they are mutually exclusive? Explain.

A- No. By definition, mutually exclusive events cannot occur together 0 B- Yes. Because P(A|B) ≠ P(A), the events A and B are not independent.

The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck.You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? (b) Find P(ace on 1st card and queen on 2nd) (c) Find P(queen on 1st card and ace on 2nd). (d) Find the probability of drawing an ace and a queen in either order.

A- No. The probability of drawing a specific second card depends on the identity of the first card. B- 4/663 C- 4/663 D- 8/663

The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck.You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? (b) Find P(ace on 1st card and ten on 2nd). (c) Find P(ten on 1st card and ace on 2nd). (d) Find the probability of drawing an ace and a ten in either order.

A- No. The probability of drawing a specific second card depends on the identity of the first card. B- 4/663 C- 4/663 D- 8/663

You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? (b) Find P(3 on 1st card and 10 on 2nd). (c) Find P(10 on 1st card and 3 on 2nd) (d) Find the probability of drawing a 10 and a 3 in either order.

A- No. The probability of drawing a specific second card depends on the identity of the first card. B- 4/663 C- 4/663 D- 8/663

You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? (b) Find P(3 on 1st card and 10 on 2nd). (c) Find P(10 on 1st card and 3 on 2nd). (d) Find the probability of drawing a 10 and a 3 in either order.

A- No. The probability of drawing a specific second card depends on the identity of the first card. B- 4/663 C- 4/663 D- 8/663

Categorize these measurements associated with a robotics company according to level: nominal, ordinal, interval, or ratio. (a) Salesperson's performance: below average, average, above average. (b) Price of company's stock (c) Names of new products (d) Temperature (°F) in CEO's private office (e) Gross income for each of the past 5 years (f) Color of product packaging

A- Ordinal B- Ratio C- Interval D- Interval E- Ratio F- Nominal

In a sales effectiveness seminar, a group of sales representatives tried two approaches to selling a customer a new automobile: the aggressive approach and the passive approach. For 1160 customers, the following record was kept: Sale No Sale Row Total Aggressive 260 320 580 Passive 464 116 580 Column Total 724 436 1160 Suppose a customer is selected at random from the 1160 participating customers. Let us use the following notation for events: A = aggressive approach, Pa = passive approach, S = sale, N = no sale. So, P(A) is the probability that an aggressive approach was used, and so on. (a) Compute P(S), P(S | A), and P(S | Pa). (b) Are the events S = sale and Pa = passive approach independent? Explain. (c) Compute P(A and S) and P(Pa and S). (d) Compute P(N) and P(N | A). (e) Are the events N = no sale and A aggressive approach independent? Explain. (f) Compute P(A or S).

A- P (S) = 724/1160 P (SlA) = 260/ 580 P (Sl Pa)= 464/580 B- No. P(S) ≠ P(S | Pa). C- P(A and S) =260/1160 P(Pa and S) =464/1160 D- P(N) =436/1160 P(N | A) =320/580 E- No. P(N) ≠ P(N | A). F- P(A or S) = 1044/1160

Suppose two events A and B are independent, with P(A) ≠ 0 and P(B) ≠ 0. By working through the following steps, you'll see why two independent events are not mutually exclusive. (a) What formula is used to compute P(A and B)? (b) Is P(A and B) ≠ 0? Explain. (c) Using the information from part (a), can you conclude that events A and B are not mutually exclusive?

A- P(A) · P(B) B- Yes. Because both P(A) and P(B) are not equal to 0, P(A and B) ≠ 0. C- Yes. Because P(A and B) ≠ 0, A and B are not mutually exclusive.

How expensive is Maui? A newspaper gave the following costs in dollars per day for a random sample of condominiums located throughout the island of Maui. 89 50 70 60 370 55 500 71 42 350 60 50 250 45 45 125 235 65 60 130 (a) Compute the mean, median, and mode for the data. (b) Does the trimmed mean more accurately reflect the general level of the daily rental costs? (c) If you were a travel agent and a client asked about the daily cost of renting a condominium on Maui, what average would you use? Explain. (d) Is there any other information about the costs that you think might be useful, such as the spread of the costs?

A- mean $136.1 median $67.5 mode $60 B- 129.3 Yes, the trimmed mean is closer to the median and mode C- Median D- The lowest and highest prices of the condominiums would also be useful.

Pax World Balanced is a highly respected, socially responsible mutual fund of stocks and bonds. Vanguard Balanced Index is another highly regarded fund that represents the entire U.S. stock and bond market (an index fund). The mean and standard deviation of annualized percent returns are shown below. The annualized mean and standard deviation are for a recent 10-years period.†. Pax World Balanced: x = 9.49%; s = 14.07%Vanguard Balanced Index: x = 9.00%; s = 12.20% (a) Compute the coefficient of variation for each fund. (b) If x represents return and s represents risk, then explain why the coefficient of variation can be taken to represent risk per unit of return. From this point of view, which fund appears to be better? Explain. (c) Compute a 75% Chebyshev interval around the mean for each fund. (d) Use the intervals to compare the two funds. As usual, past performance does not guarantee future performance.

A- Pax 148.3 % VanguardCV 135.6 % B- Since the CV is s/x we can say that the CV represents the risk per unit of return; the Vanguard fund appears to be better because the CV is smaller. C- Pax Lower Limit- -18.65 Upper Limit- 37.63 Vanguard Lower Limit- -15.4 Upper Limit- 33.4 D- Vanguard has a narrower range of returns, with less downside, but also less upside.

Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the 30 of the lower 48 states, the percentage loss of wetlands per state is as follows. (a) Make a stem-and-leaf display of these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.) (B) How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.)

A- Percent of Wetlands Lost 0- 9 1- NONE 2- 0 4 7 3- 0 3 5 5 7 8 8 4- 2 5 5 5 8 5- 0 0 0 1 5 9 9 6- 0 8 7- 3 8- 3 7 7 9- 0 B- There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands. These data are fairly symmetric, perhaps slightly skewed right. The percentages are concentrated from 20% to 60%.

(a) The video discusses a survey conducted by FreeCreditScore.com that found that when choosing a long term partner, respondents ranked financial responsibility as important as what characteristic of the potential partner? (b) What type of variable is a credit score? (c) A positive correlation (or relationship) between two variables means that as one increases, the other increases. In contrast, a negative correlation means that as one increases, the other decreases. If a higher credit score indicates a better credit history, then the video implies that the correlation between credit scores of a partner and the number of years the relationship with that partner lasts ("relationship longevity") is which of the following?

A- Physical Attractiveness B- Quantitative C- Positive

Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio. (a) Length of time to complete an exam (b) Time of first class (c) Major field of study (d)Course evaluation scale: poor, acceptable, good (e) Score on last exam (based on 100 possible points) (f) Age of student

A- Ratio B- Interval C- Nominal D- Ordinal E- Ratio F- Ratio

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 17, 14, 8, 9, 10. (a) Use the defining formula, the computation formula, or a calculator to compute s (b) Multiply each data value by 5 to obtain the new data set 85, 70, 40, 45, 50. Compute s. (c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c? (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 3.1 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? (e) Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers?

A- S= 3.7815 B- S= 18.9077 C- Multiplying each data value by the same constant c results in the standard deviation being |c| times as large. D- No E- S=4.96 km

Which technique for gathering data (sampling, experiment, simulation, or census) do you think was used in the following studies? (a) An analysis of a sample of 31,000 patients from New York hospitals suggests that the poor and the elderly sue for malpractice at one-fifth the rate of wealthier patients. (b) The effects of wind shear on airplanes during both landing and takeoff were studied by using complex computer programs that mimic actual flight. (c) A study of all league football scores attained through touchdowns and field goals was conducted by the National Football League to determine whether field goals account for more scoring events than touchdowns (d) An Australian study included 588 men and women who already had some precancerous skin lesions. Half got skin cream containing a sunscreen with a sun protection factor of 17; half got an inactive cream. After 7 months, those using the sunscreen with the sun protection had fewer precancerous skin lesions

A- Sampling B- Simulation C- Census D- Experiment

Consider a family with 4 children. Assume the probability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5, and that the events "boy" and "girl" are independent. (a) List the equally likely events for the gender of the 4 children, from oldest to youngest. (Let M represent a boy (male) and F represent a girl (female). (b) What is the probability that all 4 children are male? (c) Notice that the complement of the event "all four children are male" is "at least one of the children is female." Use this information to compute the probability that at least one child is female.

A- Select all B- 1/16 C- 15/16

The Grand Canyon and the Colorado River are beautiful, rugged, and sometimes dangerous. Thomas Myers is a physician at the park clinic in Grand Canyon Village. Dr. Myers has recorded (for a 5-year period) the number of visitor injuries at different landing points for commercial boat trips down the Colorado River in both the Upper and Lower Grand Canyon (a) Compute the mean, median, and mode for injuries per landing point in the Upper Canyon. (Enter your answers to one decimal place.) (b) Compute the mean, median, and mode for injuries per landing point in the Lower Canyon. (Enter your answers to one decimal place.) (c) Compare the results of parts (a) and (b). (d) The Lower Canyon stretch had some extreme data values. Compute a 5% trimmed mean for this region, and compare this result to the mean for the Upper Canyon computed in part (a). (Enter your answer to 2 decimal places.)

A- mean 3.27 median 3 mode 3 B- mean 4.21 median 2 mode 1 C- The Lower Canyon mean is greater, while the median and mode are less. D- 3.75 The trimmed mean is closer to the Upper Canyon mean.

An important part of employee compensation is a benefits package, which might include health insurance, life insurance, child care, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefits packages available in private businesses in Hawaii. You want a sample size of 100. Some sampling techniques are described below. Categorize each technique as simple random sample, stratified sample, systematic sample, cluster sample, or convenience sample. (a) Assign each business in the Island Business Directory a number, and then use a random-number table to select the businesses to be included in the sample. (b) Use postal ZIP Codes to divide the state into regions. Pick a random sample of 10 ZIP Code areas and then include all the businesses in each selected ZIP Code area. (c) Send a team of five research assistants to Bishop Street in downtown Honolulu. Let each assistant select a block or building and interview an employee from each business found. Each researcher can have the rest of the day off after getting responses from 20 different businesses (d) Use the Island Business Directory. Number all the businesses. Select a starting place at random, and then use every 50th business listed until you have 100 businesses. (e) Group the businesses according to type: medical, shipping, retail, manufacturing, financial, construction, restaurant, hotel, tourism, other. Then select a random sample of 10 businesses from each business type.

A- Simple Random Sample B- Cluster Sample C- Convenience Sample D- Systematic Sample E- Stratified Sample

Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. It wishes to use a sample of such patients. Several sampling techniques are described below. Categorize each technique as simple random sample, stratified sample, systematic sample, cluster sample, or convenience sample. (a) Obtain a list of patients discharged from all MMH facilities. Divide the patients according to length of hospital stay (2 days or less, 3-7 days, 8-14 days, more than 14 days). Draw simple random samples from each group. (b) Obtain lists of patients discharged from all MMH facilities. Number these patients, and then use a random-number table to obtain the sample. (c) Randomly select some MMH facilities from each of five geographic regions, and then include all the patients on the discharge lists of the selected hospitals. (d) At the beginning of the year, instruct each MMH facility to survey every 500th patient discharged. (e) Instruct each MMH facility to survey 10 discharged patients this week and send in the results.

A- Stratified Sample B- Simple Random Sample C- Cluster Sample D- Systematic Sample E- Convenience Sample

In each of the following situations, the sampling frame does not match the population, resulting in undercoverage. Give examples of population members that might have been omitted. (a) The population consists of all 250 students in your large statistics class. You plan to obtain a simple random sample of 30 students by using the sampling frame of students present next Monday. (Select all that apply.) (b) The population consists of all 15-year-olds living in the attendance district of a local high school. You plan to obtain a simple random sample of 200 such residents by using the student roster of the high school as the sampling frame. (Select all that apply.)

A- Students who are on a school trip cannot be sampled. Students who are out sick cannot be sampled. Students who are skipping class cannot be sampled. B- Dropouts cannot be sampled. Home-schooled students cannot be sampled.

Consider a data set of 15 distinct measurements with mean A and median B. (a) If the highest number were increased, what would be the effect on the median and mean? Explain. (b) If the highest number were decreased to a value still larger than B, what would be the effect on the median and mean? (c) If the highest number were decreased to a value smaller than B, what would be the effect on the median and mean?

A- The mean would increase while the median would remain the same. B- The mean would decrease while the median would remain the same. C- Both the mean and median would decrease.

The ogives shown are based on U.S. Census data and show the average annual personal income per capita for each of the 50 states. The data are rounded to the nearest thousand dollars. (a) How were the percentages shown in graph (ii) computed? (b) How many states have average per capita income less than 37.5 thousand dollars? (c) How many states have average per capita income between 42.5 and 52.5 thousand dollars? (d) What percentage of the states have average per capita income more than 47.5 thousand dollars?

A- The percentages in graph (ii) were computed by dividing each of the cumulative frequencies in graph (i) by 50 and then converting those values into percents B- 34 C- 5 D- 4%

Which technique for gathering data (observational study or experiment) do you think was used in the following studies? (a) The Colorado Division of Wildlife netted and released 774 fish at Quincy Reservoir. There were 219 perch, 315 blue gill, 83 pike, and 157 rainbow trout. (b) The Colorado Division of Wildlife caught 41 bighorn sheep on Mt. Evans and gave each one an injection to prevent heartworm. A year later, 38 of these sheep did not have heartworm, while the other three did. (c) The Colorado Division of Wildlife imposed special fishing regulations on the Deckers section of the South Platte River. All trout under 15 inches had to be released. A study of trout before and after the regulation went into effect showed that the average length of a trout increased by 4.2 inches after the new regulation. (d) An ecology class used binoculars to watch 23 turtles at Lowell Ponds. It was found that 18 were box turtles and 5 were snapping turtles.

A- This is an observational study because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured. B- This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured. C- This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured D- This is an observational study because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured.

What is the average miles per gallon (mpg) for all new hybrid small cars? Using Consumer Reports, a random sample of such vehicles gave an average of 35.7 mpg. (a) Identify the variable. (b) Is the variable quantitative or qualitative? (c) What is the implied population?

A- miles per gallon B- quantitative C- all new hybrid small cars

Suppose you are assigned the number 1, and the other students in your statistics class call out consecutive numbers until each person in the class has his or her own number. (a) Explain how you could get a random sample of four students from your statistics class. (Select all that apply.) (b) Explain why the first four students walking into the classroom would not necessarily form a random sample. (Select all that apply.) (c) Explain why four students coming in late would not necessarily form a random sample. (Select all that apply.) (d) Explain why four students sitting in the back row would not necessarily form a random sample. (Select all that apply.) (e) Explain why the four tallest students would not necessarily form a random sample. (Select all that apply.)

A- Use a computer or random-number table to randomly select four students after numbers are assigned. B- Perhaps they are students that had a class immediately prior to this one. Perhaps they are excellent students who make a special effort to get to class early. Perhaps they are students with lots of free time and nothing else to do. Perhaps they are students that needed less time to get to class . C- Perhaps they are lazy students that don't want to attend class. Perhaps they are busy students who are never on time to class. Perhaps they are students that had a prior class go past scheduled time. Perhaps they are students that need more time to get to class. D- Perhaps students in the back row are introverted. Perhaps students in the back row do not pay attention in class. Perhaps students in the back row came to class early. Perhaps students in the back row came to class late. E- Perhaps tall students generally attend more classes. Perhaps tall students generally are healthier. Perhaps tall students generally sit together. Perhaps tall students generally are athletes.

For each of the following situations, explain why the combinations rule or the permutations rule should be used. (a) Determine the number of different groups of 5 items that can be selected from 12 distinct items. (b) Determine the number of different arrangements of 5 items that can be selected from 12 distinct items.

A- Use the combinations rule, since only the items in the group is of concern. B- Use the permutations rule, since the number of arrangements within each group is of interest.

A die is a cube with dots on each face. The faces have 1, 2, 3, 4, 5, or 6 dots. The table below is a computer simulation (from the software package Minitab) of the results of rolling a fair die 20 times. (a) Assume that each number in the table corresponds to the number of dots on the upward face of the die. Is it appropriate that the same number appears more than once? Why? Yes, the outcome of the die roll can repeat. (b) What is the outcome of the fifth roll? (Assume that the data are given sequentially and Row 1 was filled first.) (c) If we simulate more rolls of the die, do you expect to get the same sequence of outcomes? Why or why not?

A- Yes, the outcome of the die roll can repeat. B- 5 C- No, because the process is random.

Consider the students in your statistics class as the population and suppose they are seated in four rows of 10 students each. To select a sample, toss a coin. If it comes up heads, you use the 20 students sitting in the first two rows as your sample. If it comes up tails, you use the 20 students sitting in the last two rows as your sample. (a) Does every student have an equal chance of being selected for the sample? Explain. (b) Is it possible to include students sitting in row 3 with students sitting in row 2 in your sample? Is your sample a simple random sample? Explain. (c) Describe a process you could use to get a simple random sample of size 20 from a class of size 40.

A- Yes, your seating location and the randomized coin flip ensure equal chances of being selected. B- No, it is not possible with this described method of selection No, this is not a simple random sample. It is a cluster sample. C- Assign each student a number 1, 2, . . . , 40 and use a computer or a random-number table to select 20 students.

You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck. (a) Are the outcomes on the two cards independent? Why? (b) Find P(3 on 1st card and 10 on 2nd). (c) Find P(10 on 1st card and 3 on 2nd). (d) Find the probability of drawing a 10 and a 3 in either order.

A- Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card. B- 1/169 C- 1/169 D- 2/169

You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck. (a) Are the outcomes on the two cards independent? Why? (b) Find P(ace on 1st card and king on 2nd). (c) Find P(king on 1st card and ace on 2nd). (d) Find the probability of drawing an ace and a king in either order.

A- Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card. B- 1/169 C- 1/169 D- 2/169

You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck. (a) Are the outcomes on the two cards independent? Why?No. The probability of drawing a specific second card depends on the identity of the first card. (b) Find P(3 on 1st card and 10 on 2nd). (c) Find P(10 on 1st card and 3 on 2nd). (d) Find the probability of drawing a 10 and a 3 in either order.

A- Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card. B- 1/169 C- 1/169 D- 2/169

You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck. (a) Are the outcomes on the two cards independent? Why?No. The probability of drawing a specific second card depends on the identity of the first card. (b) Find P(ace on 1st card and king on 2nd). (c) Find P(king on 1st card and ace on 2nd). (d) Find the probability of drawing an ace and a king in either order.

A- Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card. B- 1/169 C- 1/169 D- 2/169

Consider the following. (a) Explain why −0.41 cannot be the probability of some event. (b) Explain why 1.21 cannot be the probability of some event. (c) Explain why 120% cannot be the probability of some event. (d) Can the number 0.56 be the probability of an event? Explain.

A- a probability must be between zero and ne B- A probability must be between zero and one. C- A probability must be between zero and one. D- Yes, it is a number between 0 and 1.

Consider the following ordered data. 6 9 9 10 11 11 12 13 14 (a) Find the low, Q1, median, Q3, and high. (b) Find the interquartile range.

A- low 6 Q1 9 median 11 Q3 12.5 high 14 B- 3.5

In this problem, we explore the effect on the mean, median, and mode of adding the same number to each data value. Consider the data set 4, 4, 5, 8, 12. (a) Compute the mode, median, and mean. (Enter your answers to one decimal place.) (b) Add 3 to each of the data values. Compute the mode, median, and mean. (Enter your answers to one decimal place.) (c) Compare the results of parts (a) and (b). In general, how do you think the mode, median, and mean are affected when the same constant is added to each data value in a set?

A- mode 4 median 5 mean 6.6 B- mode 7 median 8 mean 9.6 C- Adding the same constant c to each data value results in the mode, median, and mean increasing by c units.

Consider the following numbers. 23455 (a) Compute the mode, median, and mean. (b) If the numbers represented codes for the colors of T-shirts ordered from a catalog, which average(s) would make sense? (Select all that apply.) (c) If the numbers represented one-way mileages for trails to different lakes, which average(s) would make sense? (Select all that apply.) (d) Suppose the numbers represent survey responses from 1 to 5, with 1 = disagree strongly, 2 = disagree, 3 = agree, 4 = agree strongly, and 5 = agree very strongly. Which average(s) make sense? (Select all that apply.)

A- mode 5 median 4 mean 3.8 B- Mode C- mode median mean D- mode median

In this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. Consider the following data set. 5, 5, 6, 9, 13 (a) Compute the mode, median, and mean. (b) Multiply each data value by 7. Compute the mode, median, and mean (c) Compare the results of parts (a) and (b). In general, how do you think the mode, median, and mean are affected when each data value in a set is multiplied by the same constant? (d) Suppose you have information about average heights of a random sample of airline passengers. The mode is 67 inches, the median is 72 inches, and the mean is 75 inches. To convert the data into centimeters, multiply each data value by 2.54. What are the values of the mode, median, and mean in centimeters? (Enter your answers to two decimal places.)

A- mode 5 median 6 mean 7.6 B- mode 35 median 42 mean 53.2 c- Multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c. D- mode 170.18 cm median 182.88 cm mean 190.5 cm

Consider the following types of data that were obtained from a random sample of 49 credit card accounts. Identify all the averages (mean, median, or mode) that can be used to summarize the data. (Select all that apply.) (a) Outstanding balance on each account. (b) Name of credit card (e.g., MasterCard, Visa, American Express, etc.). (c) Dollar amount due on next payment.

A- mode, median, mean B- mode C- mode, median, mean

Government agencies carefully monitor water quality and its effect on wetlands.† Of particular concern is the concentration of nitrogen in water draining from fertilized lands. Too much nitrogen can kill fish and wildlife. Twenty-eight samples of water were taken at random from a lake. The nitrogen concentration (milligrams of nitrogen per liter of water) was determined for each sample. (a) Identify the variable. (B) What is the implied population?

A- nitrogen concentration- quanitative B- the entire lake

Suppose a weather app states that the possibility of rain today is 50%. a) what is the complement of the event "rain today"? b) What is the probability of the complement?

A- no rain today B- .50

The archaeological site of Tara is more than 4000 years old. Tradition states that Tara was the seat of the high kings of Ireland. Because of it's archaeological importance, Tara has received extensive study (Reference: Tara: An Archaeological Survey by Conor Newman, Royal Irish Academy, Dublin). Suppose an archaeologist wants to estimate the density of ferromagnetic artifacts in the Tara region. For this purpose, a random sample of 55 plots, each of size 100 square meters, is used. The number of ferromagnetic artifacts for each plot is determined. (a) Identify the variable. (b) Is the variable quantitative or qualitative? (c) What is the implied population?

A- number of ferromagnetic artifacts per 100 square meters B- quantitative C- the entire Tara region

Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims. (a) Would you say the correlation is low, moderate, or strong? positive or negative? (b) Use a calculator to verify that Σx = 132, Σx2 = 6620, Σy = 149, Σy2 = 4765, and Σxy = 2959. Compute r. (c) As x increases, does the value of r imply that y should tend to increase or decrease? Explain.

A- strong and negative B- r= 0 C- Given our value of r, y should tend to decrease as x increases

Describe the relationship between two variables when the correlation coefficient r is one of the following. (a) near -1 (b) near 0 (c) near 1

A- strong negative linear correlation B- weak or no linear correlation C- Strong positive linear correlation

(a) The video indicates which of the following is an acceptable alternative to washing your hands for 20 seconds with respect to preventing illness? (b) The video urges people to wash their hands to reduce the likelihood (that is, the probability) of contracting diseases. What does this imply? (c) Suppose a student has had one illness in the last month, but her roommate has had two. With no other information about this student or her roommate, given the information in this video, what is your best guess about the student's and her roommate's hand-washing habits? (d) Suppose you have already had a disease, D, and doctors tell you that you cannot contract it again. Assuming the doctors are correct, which of the following probability statements about your contracting the disease is correct, where P(D) stands for "the probability of contracting the disease"? (Hint: A probability is a value between 0 and 1, where 0 means that the event will not occur with certainty and 1 means the event will occur, with certainty.)

A- using hand sanitizer with at least 60% alcohol B- The probability of contracting a disease is lower if you wash your hands than if you don't wash your hands. That is: P(disease if you wash your hands) < P(disease if you don't wash your hands) C- The student does the best job of washing her hands. D- P(D) = 0

You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? (b) Find P(1 on green die and 2 on red die). (c) Find P(2 on green die and 1 on red die). (d) Find P((1 on green die and 2 on red die) or (2 on green die and 1 on red die)).

A- yes B- 1/36 C- 1/36 D- 1/18

You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? (b) Find P(1 on green die and 5 on red die). (c) Find P(5 on green die and 1 on red die). (d) Find P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)).

A- yes B- 1/36 2- 1/36 D- 1/18

Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). X 25 42 29 47 23 40 34 52 y 32 17 24 13 29 17 21 14 Complete parts (a) through (e), given Σx = 292, Σy = 167, Σx2 = 11,428, Σy2 = 3825, Σxy = 5610, and r ≈ −0.9504. (a) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (b) Find x, and y. Then find the equation of the least-squares line ŷ = a + bx. (c) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (d) Suppose a car weighs x = 37 (hundred pounds). What does the least-squares line forecast for y = miles per gallon?

A- Σx = 292 Σy = 167 Σx2 = 11,428 Σy2 = 3825 Σxy = 5610 r = -0.9504 B- x = 36.5 y = 20.875 ŷ = 43.8889 + -0.6305 C- r2=0.9032 explained 90.32% unexplained 9.68 % D- 20.56 mpg

You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms). x 1 4 10 16 26 36 y 42 54 75 100 150 200 Complete parts (a) through (e), given Σx = 93, Σy = 621, Σx2 = 2345, Σy2 = 82,805, Σxy = 13,708, and r ≈ 0.9977. (a) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r (b) Find x, and y. Then find the equation of the least-squares line = a + bx. (c) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (d) The calves you want to buy are 16 weeks old. What does the least-squares line predict for a healthy weight?

A- Σx =93 Σy =621 Σx2 =2345 Σy2 =82,805 Σxy =13,708 r =0.9977 B- x= 15.5 y= 103.5 = 33.4627 + 4.5185 x C- r2 =0.9954 explained 99.54% unexplained 0.46 % D- 105.76 kg

For mallard ducks and Canada geese, what percentage of nests are successful (at least one offspring survives)? Studies in Montana, Illinois, Wyoming, Utah, and California give the following percentages of successful nests x: Percentage success for mallard duck nests 80 62 26 14 26 y: Percentage success for Canada goose nests39 36 69 57 60 (a) Use a calculator to verify that Σx = 208; Σx2 = 11,792; Σy = 261; and Σy2 = 14,427. (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x, the percent of successful mallard nests. (c) Use the results of part (a) to compute the sample mean, variance, and standard deviation for y, the percent of successful Canada goose nests. (d) Use the results of parts (b) and (c) to compute the coefficient of variation for successful mallard nests and Canada goose nests. (e) Write a brief explanation of the meaning of these numbers. What do these results say about the nesting success rates for mallards compared to Canada geese? (f) Would you say one group of data is more or less consistent than the other? Explain.

A- Σx208 Σx211,792 Σy261 Σy214,427 B- x-41.6 s-2784.8 s2-8.0143 C- y-52.2 s2-200.7 s-14.1669 D- CV67.3 % 27.1% E- The CV is the ratio of the standard deviation to the mean; the CV for mallard nests is higher F- The y data group is more consistent because the standard deviation is smaller.

An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a given neighborhood, and let y represent the number of entry-level jobs in the same neighborhood. A sample of six Denver neighborhoods gave the following information (units in hundreds of jobs). x 17 34 48 28 50 25 y 1 2 5 5 9 3 Complete parts (a) through (e), given Σx = 202, Σy = 25, Σx2 = 7658, Σy2 = 145, Σxy = 990, and r ≈ 0.7928. (a) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (b) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (c) For a neighborhood with x = 43 hundred jobs, how many are predicted to be entry level jobs?

A- Σx=202 Σy=25 Σx2=7658 Σy2=145 Σxy=990 r=0.7928 B- r2=0.6285 explained 62.85% unexplained 37.15% C- 5.78 hundred jobs

According to the video, if you are given the choice of three cups in which a prize is under one of the cups, you should do which of the following?

After you have chosen your cup and you are shown which of the other two cups does not have the prize, you should switch your choice to the cup that you were not shown.

An agricultural study is comparing the harvest volume of two types of barley. The site for the experiment is bordered by a river. The field is divided into eight plots of approximately the same size. The experiment calls for the plots to be blocked into four plots per block. Then, two plots of each block will be randomly assigned to one of the two barley types. Two blocking schemes are shown below, with one block indicated by the white region and the other by the grey region. Which blocking scheme, A or B, would be best? Explain.

Based on the information, Scheme A will be better because the block bordering the river is different from the block away from the river.

You need to know the number of different arrangements possible for five distinct letters. You decide to use the permutations rule, but your friends tells you to use 5!. Who is correct? Explain.

Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time.

When drawing a scatter diagram, along which axis is the explanatory variable placed? Along which axis is the response variable placed?

horizontal axis; vertical axis

If there are three different samples of the same size from a set population, is it possible to get three different values for the same statistic?

Data from samples may vary from sample to sample, and so corresponding sample statistics may vary from sample to sample.

A data set has values ranging from a low of 10 to a high of 52. What's wrong with using the class limits 10-19, 20-29, 30-39, 40-49 for a frequency table?

Each data value must fall into one class. The data values of 50 and above do not have a class.

The town of Butler, Nebraska, decided to give a teacher-competency exam and defined the passing scores to be those in the 70th percentile or higher. The raw test scores ranged from 0 to 100. Was a raw score of 82 necessarily a passing score? Explain.

No, it might have a percentile rank less than 70.

Explain the difference between a stratified sample and a cluster sample.

In a stratified sample, random samples from each strata are included. In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included.

Explain the difference between a simple random sample and a systematic sample. (Select all that apply.)

In a systematic sample, the only samples possible are those including every kth item from the random starting position. In a simple random sample, every sample of size n has an equal chance of being included.

List three methods of assigning probabilities.

Intuition, equally likely outcomes, relative frequency

If two variables have a negative linear correlation, is the slope of the least-squares line positive or negative?

Negative

For a set population, does a parameter ever change?

Never

On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5. If you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss? Explain.

No, each outcome is equally likely regardless of the previous outcome.9

Over the past few years, there has been a strong positive correlation between the annual consumption of diet soda drinks and the number of traffic accidents. (a) Do you think increasing consumption of diet soda drinks causes traffic accidents? Explain your answer.

No. A strong correlation does not imply causation.

If two events are mutually exclusive, can they occur concurrently? Explain.

No. By definition, mutually exclusive events cannot occur together.

A study of college graduates involves three variables: income level, job satisfaction, and one-way commute times to work. List some ways the variables might be confounded. (Select all that apply.)

One-way commute times may be long because affordable housing is distant from the job. People may have a career following their passion, but have a low income or a long commute. A working spouse could affect all three variables. People might be very satisfied with their career as long as the income is high.

Let P(x, y) be the probability of choosing an x-colored ball on the first draw and a y-colored ball on the second draw. Compute the probability for each outcome of the experiment.

P(R, R) =20/110 P(R, B) =25/110 P(R, Y) =5/110 P(B, R) =25/110 P(B, B) =20/110 P(B, Y) =5/110 P(Y, R) =5/110 P(Y, B) =5/110

A personnel office is gathering data regarding working conditions. Employees are given a list of five conditions that they might want to see improved. They are asked to select the one item that is most critical to them. Which type of graph, circle graph or Pareto chart, would be the most useful for displaying the results of the survey? Why?

Pareto chart, because it shows the items in order of importance to employees.

What is the main difference between a situation in which the use of the permutations rule is appropriate and one in which the use of the combinations rule is appropriate?

Permutations count the number of different arrangements of r out of n items, while combinations count the number of groups of r out of n items.

Are data at the nominal level of measurement quantitative or qualitative?

Qualitative

What symbol is used for the standard deviation when it is a sample statistic? What symbol is used for the standard deviation when it is a population parameter?

Sample statistic: s. Population parameter: 𝜎

Driving would be more pleasant if we didn't have to put up with the bad habits of other drivers. A newspaper reported the results of a Valvoline Oil Company survey of 500 drivers in which the drivers marked their complaints about other drivers. The top complaints turned out to be tailgating, marked by 24% of the respondents; not using turn signals, marked by 19%; being cut off, marked by 13%; other drivers driving too slowly, marked by 9%; and other drivers being inconsiderate marked by 6%. Could this information as reported be put in a circle graph? Why or why not?

Since the percentages do not add to 100%, a circle graph cannot be used. If we create an "other" category and assume that all other respondents fit this category, then a circle could be created.

Marcie conducted a study of the cost of breakfast cereal. She recorded the costs of several boxes of cereal. However, she neglected to take into account the number of servings in each box. Someone told her not to worry because she just had some sampling error. Comment on that advice.

The advice is wrong. A sampling error only accounts for the difference in results based on the use of a sample rather than the entire population

A data set has values ranging from a low of 10 to a high of 50. The class width is to be 10. What's wrong with using the class limits 10-20, 21-31, 32-42, 43-53 for a frequency table with a class width of 10?

The classes listed have a class width of 11.

A data set has values ranging from a low of 10 to a high of 50. What's wrong with using the class limits 10-20, 20-30, 30-40, 40-50 for a frequency table?

The classes overlap so that some data values, such as 20, fall within two classes

Why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? Hint: Consider how much the data in the respective sets differ from the mean.

The data change between data sets (i) and (ii) increased the squared difference Σ(x - x)2 by more than data sets (ii) and (iii).

The guys in the video set up an experiment to compare the two game strategies, just as a researcher might set up an experiment to compare the effectiveness of two treatments. Which of the following statements is true about how these experiments are similar?

The guys in the video and a researcher studying treatments conduct their experiment multiple times so that they can learn what happens across several cases.

The guys in the video set up an experiment to compare the two game strategies, just as a researcher might set up an experiment to compare the effectiveness of two treatments. Which of the following statements is true about how these experiments are different?

The guys in the video know what the actual ANSWER should be if they were to conduct their experiment with or on all possible cases, while the researcher studying treatments does not.

When a distribution is mound-shaped symmetrical, what is the general relationship among the values of the mean, median, and mode?

The mean, median, and mode are approximately equal.

Suppose two variables are negatively correlated. Does the response variable increase or decrease as the explanatory variable increases?

The response variable will decrease as the explanatory variable increases.

Suppose two variables are positively correlated. Does the response variable increase or decrease as the explanatory variable increases?

The response variable will increase as the explanatory variable increases.

Can you wiggle your ears? Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can wiggle their ears. How can your result be thought of as an estimate for the probability that a person chosen at random can wiggle his or her ears? Comment: National statistics indicate that about 13% of Americans can wiggle their ears

The resulting relative frequency can be used as an estimate of the true probability of all Americans who can wiggle their ears.

What is the relationship between the variance and the standard deviation for a sample data set?

The standard deviation is the square root of the variance.

Clayton and Timothy took different sections of Introduction to Economics. Each section had a different final exam. Timothy scored 83 out of 100 and had a percentile rank in his class of 72. Clayton scored 85 out of 100 but his percentile rank in his class was 70. Who performed better with respect to the rest of the students in the class, Clayton or Timothy? Explain your answer.

Timothy, since his percentile score is higher.

When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?

We are extrapolating. Extrapolation is dangerous because the pattern of data may change outside the x range.

Suppose there are 30 people at a party. Do you think any two share the same birthday? Let's use the random-number table to simulate the birthdays of the 30 people at the party. Ignoring leap year, let's assume that the year has 365 days. Number the days, with 1 representing January 1, 2 representing January 2, and so forth, with 365 representing December 31. Draw a random sample of 30 days (with replacement). These days represent the birthdays of the people at the party. Would you expect any two of the birthdays to be the same?

We do expect at least one match on birthdays on over 50% of the times we run this experiment.

In the Aloha state, you are very unlikely to be murdered! However, it is considerably more likely that your house might be burgled, your car might be stolen, or you might be punched in the nose. That said, Hawaii is still a great place for a vacation or, if you are very lucky, to live. The following numbers represent the crime rates per 100,000 population in Hawaii: murder, 3.6; rape, 40.4; robbery, 78.3; house burglary, 884.6; motor vehicle theft, 547.7; assault, 134.3. Could the information as reported be displayed as a circle graph? Explain. Hint: Other forms of crime, such as arson, are not included in the information. In addition, some crimes might occur together.

Yes, but the graph would take into account only these particular crimes and would not indicate if multiple crimes occurred during the same incident.

When computing the standard deviation, does it matter whether the data are sample data or data comprising the entire population? Explain.

Yes. The formula for s is divided by n − 1, while the formula for 𝜎 is divided by N.

You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck. (a) Are the outcomes on the two cards independent? Why?

Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.

Which average - mean, median, or mode - is associated with the standard deviation?

mean

Find the mean, median, and mode of the data set. 7 2 6 2 4 3

mean 4 median 3.5 mode 2

What symbol is used for the arithmetic mean when it is a sample statistic? What symbol is used when the arithmetic mean is a population parameter?

statistic, x; parameter, 𝜇

What was the age distribution of prehistoric Native Americans? Extensive anthropological studies in the southwestern United States gave the following information about a prehistoric extended family group of 86 members on what is now a Native American reservation. For this community, estimate the mean age expressed in years, the sample variance, and the sample standard deviation. For the class 31 and over, use 35.5 as the class midpoint. (Round your answers to one decimal place.)

x=16.3 s2=132.3 s=11.5

What is the age distribution of adult shoplifters (21 years of age or older) in supermarkets? The following is based on information taken from the National Retail Federation. A random sample of 895 incidents of shoplifting gave the following age distribution. Estimate the mean age, sample variance, and sample standard deviation for the shoplifters. For the class 41 and over, use 45.5 as the class midpoint. (Round your answers to one decimal place.)

x=35.9 s2=58.5 s=7.7