Statistics - BUSI 230 - Week 1-2
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. (c) Describe a process you could use to get a simple random sample of size 20 from a class of size 40.
Assign each student a number 1, 2, . . . , 40 and use a computer or a random-number table to select 20 students.
Explain the difference between a stratified sample and a cluster sample. (Select all that apply.)
In a cluster sample, the clusters to be included are selected at random and then all members of each selected cluster are included. In a stratified sample, random samples from each strata are included.
Consider the mode, median, and mean. (a) Which average represents the middle value of a data distribution?
median
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. (b) Explain why the first four students walking into the classroom would not necessarily form a random sample. (Select all that apply.)
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 had a class immediately prior to this one. Perhaps they are students that needed less time to get to class.
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.
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.
simple random sample
Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) Without doing any computations, order the data sets according to increasing value of standard deviations.
(i), (ii), (iii)
A data set with whole numbers has a low value of 20 and a high value of 96. Find the class width for a frequency table with seven classes.
11
At one hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were as follows. 29 8 11 20 31 42 33 48 18 14 13 29 35 32 34 17 26 37 14 42 Find the interquartile range.
19
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 16, 8, 17, 5, 9. Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)
3.68
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. (b) How many states have average per capita income less than 37.5 thousand dollars?
36
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 16, 8, 17, 5, 9. (b) Multiply each data value by 5 to obtain the new data set 85, 60, 35, 60, 50. Compute s. (Round your answer to one decimal place.)
36.7
Consider the data set. 2, 4, 5, 7, 8 (a) Find the range.
6
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.
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 2, 2, 3, 6, 10. (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?
Adding the same constant c to each data value results in the mode, median, and mean increasing by c units.
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. 14, 17, 15, 10, 4 (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?
Adding the same constant c to each data value results in the standard deviation remaining the same.
Look at the histogram below, which shows mileage, in miles per gallon (mpg), for a random selection of older passenger cars.† (b) Jose looked at the raw data and discovered that the 54 data values included both the city and highway mileages for 27 cars. He used the city mileages for the 27 cars to make the histogram below. Using this information and the histograms shown above, construct a frequency table for the highway mileages of the same cars. Use class boundaries 16.5, 20.5, 24.5, 28.5, 32.5, 36.5, and 40.5.
Class Boundaries: 16.5-20.5,20.5-24.5,24.5-28.5,28.5-32.5,32.5-36.5,36.5-40.5 Frequency: 2,3,3,12,6,1
What is the difference between a class boundary and a class limit? (Select all that apply.)
Class limits are possible data values. Class boundaries are values halfway between the upper class limit of one class and the lower class limit of the next. Class limits specify the span of data values that fall within a class. Class boundaries are not possible data values.
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. (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.)
Dropouts cannot be sampled. Home-schooled students cannot be sampled.
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. 2, 2, 3, 6, 10 (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?
Multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c.
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 16, 8, 17, 5, 9. (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 2.3 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations?
No
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. (b) Does the median change? Explain.
No, changing the extreme data values does not affect the median.
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. (b) Is it possible to include students sitting in row 3 with students sitting in row 2 in your sample?
No, it is not possible with this described method of selection.
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.
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?
No, since 80 is less than 2.5 standard deviations above the mean.
Suppose you are looking at the 2006 results of how the Echo generation classified specified items as either luxuries or necessities. Do you expect the results to reflect how the Echo generation would classify items in 2020? Explain.
No, the generation will have aged by 14 years and their perception of items as necessities or luxuries might well have changed by then.
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.
No, the sum of the data does not change.
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
No, they are at the nominal level as there is no apparent ordering in the responses.
Consider these number assignments for category items describing usefulness of customer service. 1 = not helpful; 2 = somewhat helpful; 3 = very helpful; 4 = extremely helpful
No, they are at the nominal level as there is no apparent ordering in the responses.
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. Is your sample a simple random sample? Explain.
No, this is not a simple random sample. It is a cluster sample.
What about at the interval level or higher? Explain.
No, while the data has an ordering, and the data can be compared to each other, the differences don't mean anything.
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.
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. (d) Explain why four students sitting in the back row would not necessarily form a random sample. (Select all that apply.)
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. Perhaps students in the back row are introverted.
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. (e) Explain why the four tallest students would not necessarily form a random sample. (Select all that apply.)
Perhaps tall students generally are healthier. Perhaps tall students generally sit together. Perhaps tall students generally are athletes. Perhaps tall students generally attend more classes.
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. (c) Explain why four students coming in late would not necessarily form a random sample. (Select all that apply.)
Perhaps they are students that had a prior class go past scheduled time. Perhaps they are busy students who are never on time to class. Perhaps they are lazy students that don't want to attend class. Perhaps they are students that need more time to get to class.
You are interested in the weights of backpacks students carry to class and decide to conduct a study using the backpacks carried by 30 students. (b) Do you think each student asked will allow you to weigh his or her backpack?
Some students may refuse to allow the weighing.
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.)
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.
How old are professional football players? The 11th Edition of The Pro Football Encyclopedia gave the following information. Random sample of pro football player ages in years: 24 23 25 23 30 29 28 26 33 29 24 37 25 23 22 27 28 25 31 29 25 22 31 29 22 28 27 26 23 21 25 21 25 24 22 26 25 32 26 29 (b) Compare the averages. Does one seem to represent the age of the pro football players most accurately? Explain.
The averages are very close. The median seems to represent the ages most accurately.
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.
Which technique for gathering data (observational study or experiment) do you think was used in the following studies? (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.
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.
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.
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.)
Use a computer or random-number table to randomly select four students after numbers are assigned.
You are interested in the weights of backpacks students carry to class and decide to conduct a study using the backpacks carried by 30 students. (a) Give some instructions for weighing the backpacks. Include unit of measure, accuracy of measure, and type of scale.
Use pounds. Round weights to the nearest pound. Since backpacks might weigh as much as pounds, you might use a high-quality bathroom scale.
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.
Yes, your seating location and the randomized coin flip ensure equal chances of being selected.
Which technique for gathering data (sampling, experiment, simulation, or census) do you think was used in the following studies? (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 (USA Today).
census
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. (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.
cluster sample
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. (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.
convenience sample
Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio. (b) Time of first class
interval
Which average - mean, median, or mode - is associated with the standard deviation?
mean
How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (°F) were taken from May to November in the vicinity of Furnace Creek. Compute the mean, median, and mode for these ground temperatures. (Enter your answers to one decimal place.) 145 150 169 172 184 181 182 184 181 169 181 166 150 143
mean: 168.4 median: 170.5 mode: 181
How old are professional football players? The 11th Edition of The Pro Football Encyclopedia gave the following information. Random sample of pro football player ages in years: 24 23 25 23 30 29 28 26 33 29 24 37 25 23 22 27 28 25 31 29 25 22 31 29 22 28 27 26 23 21 25 21 25 24 22 26 25 32 26 29 (a) Compute the mean, median, and mode of the ages. (Enter your answers to one decimal place.)
mean: 26.3 median: 25.5 mode: 25
Find the mean, median, and mode of the data set. 9 2 8 2 6 3
mean: 5 median: 4.5 mode: 2
Find the mean, median, and mode of the data set. 9 4 8 4 7
mean: 6.4 median: 7 mode: 4
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.
miles per gallon
Consider the following numbers. 2 3 4 5 5 (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.)
mode
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.) (b) Name of credit card (e.g., MasterCard, Visa, American Express, etc.).
mode
Consider the mode, median, and mean. (b) Which average represents the most frequent value of a data distribution?
mode
Consider the following numbers. 2 3 4 5 5 (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.)
mode, median
Consider the following numbers. 2 3 4 5 5 (c) If the numbers represented one-way mileages for trails to different lakes, which average(s) would make sense? (Select all that apply.)
mode, median, mean
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.
mode, median, mean
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.) (c) Dollar amount due on next payment.
mode, median, mean
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. 2, 2, 3, 6, 10 (b) Multiply each data value by 8. Compute the mode, median, and mean.
mode: 16 median: 24 mean: 36.8
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. 2, 2, 3, 6, 10 (a) Compute the mode, median, and mean.
mode: 2 median: 3 mean: 4.6
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 2, 2, 3, 6, 10. (a) Compute the mode, median, and mean. (Enter your answers to one decimal place.)
mode: 2 median: 3 mean: 4.6
Consider the following numbers. 2 3 4 5 5 (a) Compute the mode, median, and mean.
mode: 5 median: 4 mean: 3.8
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 2, 2, 3, 6, 10. (b) Add 5 to each of the data values. Compute the mode, median, and mean. (Enter your answers to one decimal place.)
mode: 7 median: 8 mean: 9.6
Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio. (d) Course evaluation scale: poor, acceptable, good
ordinal
Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio. (e) Score on last exam (based on 100 possible points)
ratio
Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio. (f) Age of student
ratio
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. (Journal of the American Medical Association).
sampling
Which technique for gathering data (sampling, experiment, simulation, or census) do you think was used in the following studies? (b) The effects of wind shear on airplanes during both landing and takeoff were studied by using complex computer programs that mimic actual flight.
simulation
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
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. (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.
stratified sample
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. (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.
systematic sample
Angela took a general aptitude test and scored in the 81st percentile for aptitude in accounting. (b) What percentage were above?
19%
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. (d) What percentage of the states have average per capita income more than 47.5 thousand dollars?
2
Consider the data set. 2, 4, 5, 7, 8 (c) Use the defining formula to compute the population standard deviation σ. (Round your answer to two decimal places.)
2.14
Consider the data set. 2, 4, 5, 7, 8 (b) Use the defining formula to compute the sample standard deviation s. (Round your answer to two decimal places.)
2.39
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. 14, 17, 15, 10, 4 (a) Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to one decimal place.)
5.1
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. 14, 17, 15, 10, 4 (b) Add 3 to each data value to get the new data set 17, 20, 18, 13, 7. Compute s. (Enter your answer to one decimal place.)
5.1
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 16, 8, 17, 5, 9. (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to one decimal place.)
5.2
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. (c) How many states have average per capita income between 42.5 and 52.5 thousand dollars?
6
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%
In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 19% of your total grade, each major test is worth 24.5%, and the final exam is worth 32%. Compute the weighted average for the following scores: 74 on the lab, 75 on the first major test, 68 on the second major test, and 81 on the final exam.
75.015
Angela took a general aptitude test and scored in the 81st percentile for aptitude in accounting. (a) What percentage of the scores were at or below her score?
81%
Commercial dredging operations in ancient rivers occasionally uncover archaeological artifacts of great importance. One such artifact is Bronze Age spearheads recovered from ancient rivers in Ireland. A recent study gave the following information regarding discoveries of ancient bronze spearheads in Irish rivers. River Bann Blackwater Erne Shannon Barrow No. of spearheads 23 5 15 36 14 (b) Make a circle graph for these data.
Bann 24.73% Blackwater 5.38% Erne 16.13% Shannon 38.71% Barrow 15.05%
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.
If you were going to apply statistical methods to analyze teacher evaluations, which question form, A or B, would be better? Form A: In your own words, tell how this teacher compares with other teachers you have had. Form B: Use the following scale to rank your teacher as compared with other teachers you have had. 1 2 3 4 5 worst below average average above average best
Form B would be better because statistical methods can be applied to the ordinal data.
What percentage of the general U.S. population have bachelor's degrees? The Statistical Abstract of the United States, 120th Edition, gives the percentage of bachelor's degrees by state. For convenience, the data are sorted in increasing order. 17 18 18 18 19 20 20 20 21 21 21 21 22 22 22 22 22 22 23 23 24 24 24 24 24 24 24 24 25 26 26 26 26 26 26 27 27 27 27 27 28 28 29 31 31 32 32 34 35 38 (b) Find the interquartile range.
IQR = 5
Explain the difference between a simple random sample and a systematic sample. (Select all that apply.)
In a simple random sample, every sample of size n has an equal chance of being included. In a systematic sample, the only samples possible are those including every kth item from the random starting position.
You are interested in the weights of backpacks students carry to class and decide to conduct a study using the backpacks carried by 30 students. (c) Do you think telling students ahead of time that you are going to weigh their backpacks will make a difference in the weights?
Informing students before class may cause students to remove items before class.
Commercial dredging operations in ancient rivers occasionally uncover archaeological artifacts of great importance. One such artifact is Bronze Age spearheads recovered from ancient rivers in Ireland. A recent study gave the following information regarding discoveries of ancient bronze spearheads in Irish rivers. River Bann Blackwater Erne Shannon Barrow No. of spearheads 23 5 15 36 14 (a) Make a Pareto chart for these data.
Largest to smallest bar graph for information. 36 23 15 14 5
A data set with whole numbers has a low value of 20 and a high value of 96. Find the class limits for a frequency table with seven classes.
Lower Class Limit: 20,31,42,53,64,75,86 Upper Class Limit: 30,41,52,63,74,85,96
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 16, 8, 17, 5, 9. (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?
Multiplying each data value by the same constant c results in the standard deviation being |c| times as large.
Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (b) 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 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?
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.
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.
Which technique for gathering data (observational study or experiment) do you think was used in the following studies? (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.
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.
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.
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.
Which technique for gathering data (observational study or experiment) do you think was used in the following studies? (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.
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.
Look at the histogram below, which shows mileage, in miles per gallon (mpg), for a random selection of older passenger cars.† (a) Is the shape of the histogram essentially bimodal?
Yes, because the histogram has two peaks.
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. (c) Is it possible for the mode to change? Explain.
Yes, depending on which data value occurs most frequently after the data are changed.
One indicator of an outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80. (b) If a data set has mean 70 and standard deviation 3, is 80 a suspect outlier?
Yes, since 80 is more than 2.5 standard deviations above the mean.
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.
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. (c) What is the implied population?
all new hybrid small cars
What percentage of the general U.S. population have bachelor's degrees? The Statistical Abstract of the United States, 120th Edition, gives the percentage of bachelor's degrees by state. For convenience, the data are sorted in increasing order. 17 18 18 18 19 20 20 20 21 21 21 21 22 22 22 22 22 22 23 23 24 24 24 24 24 24 24 24 25 26 26 26 26 26 26 27 27 27 27 27 28 28 29 31 31 32 32 34 35 38 (c) Illinois has a bachelor's degree percentage rate of about 26%. Into what quarter does this rate fall?
between the median and Q3
Which technique for gathering data (sampling, experiment, simulation, or census) do you think was used in the following studies? (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 (New England Journal of Medicine).
experiment
Consider the mode, median, and mean. (c) Which average takes all the specific values into account?
mean
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. 2, 2, 3, 6, 10 (d) Suppose you have information about average heights of a random sample of airline passengers. The mode is 64 inches, the median is 71 inches, and the mean is 72 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.)
mode: 162.56 median: 180.34 mean: 182.88
Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio. (c) Major field of study
nominal
Are data at the nominal level of measurement quantitative or qualitative?
qualitative
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. (b) Is the variable quantitative or qualitative?
quantitative
Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio. (a) Length of time to complete an exam
ratio