Quiz 1
5. Certain kinds of tumors tend to recur. The following data represent the lengths of time, in months, for a tumor to recur after chemotherapy 19181712122544625495015939433959381814455459465029121936384043411050412519392720 For this problem, use five classes. (a) Find the class width.
a 12
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. A parameter is a numerical measurement describing data from a sample. A statistic is an aspect of an individual subject or object being measured. A parameter is a numerical measurement describing data from a population. A statistic is an aspect of an individual subject or object being measured. A parameter is an aspect of an individual subject or object being measured. A statistic is a numerical measurement describing data from a sample. A parameter is an aspect of an individual subject or object being measured. A statistic is a numerical measurement describing data from a population. A parameter is a numerical measurement describing data from a sample. A statistic is a numerical measurement describing data from a population.
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 time-series graph because the pattern of stock prices over time is less relevant than the frequency of a range of closing prices. A histogram because the pattern of stock prices over time is more relevant than the frequency of a range of closing prices. A histogram because the pattern of stock prices over time is less relevant than the frequency of a range of closing prices.
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 a statistical study what is the difference between an individual and a variable? An individual is the population of interest. A variable is an aspect of an individual subject or object being measured. An individual is a member of the population of interest. A variable is a numerical measurement describing data from a population. An individual is a member of the population of interest. A variable is a numerical measurement describing data from a sample. An individual is a member of the population of interest. A variable is an aspect of an individual subject or object being measured. An individual is the population of interest. A variable is a numerical measurement describing data from a population.
An individual is a member of the population of interest. A variable is an aspect of an individual subject or object being measured.
A data set with whole numbers has a low value of 20 and a high value of 103. Find the class width for a frequency table with seven classes. Find the class limits for a frequency table with seven classes.
Class width 12
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 only one class. The classes have overlapping values. There is nothing wrong with using these class limits for the data set. The class widths are too wide and not evenly spread out over the data range of 10 to 52. Each data value must fall into one class. The data values of 50 and above do not have a class.
Each data value must fall into one class. The data values of 50 and above do not have a class.
Explain the difference between a stratified sample and a cluster sample. (Select all that apply.) In a cluster sample, every sample of size n has an equal chance of being included. In a stratified sample, every sample of size n has an equal chance of being included. In a stratified 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. In a cluster sample, the only samples possible are those including every kth item from the random starting position. In a cluster 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. In a stratified sample, the only samples possible are those including every kth item from the random starting position.
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.
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. No, they are at the nominal level as there is no apparent ordering in the responses. Yes, they are ratio data as we can order this data, take the differences and find ratios between the data values. Yes, they are interval data as we can order this data and the differences between data values are important. Yes, they are at the ordinal level as we can order the data and compare the data values to each other.
No, they are at the nominal level as there is no apparent ordering in the responses.
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 total number of important issues to employees. Pareto chart, because it shows the items in order of importance to employees. Circle chart, because it shows the total number of important issues to employees. Circle chart, because it shows the items in order of importance to employees.
Pareto chart, because it shows the items in order of importance to employees.
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? There is nothing wrong with using these class limits for a frequency table with a class width of 10. The classes overlap so that some data values fall within two classes. Each data value must fall into one class. Some data values do not have a class. The classes listed have a class width of 11.
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? Each data value must fall into one class. Some data values do not have a class. The class widths are too wide for the data range of 10 to 50. The classes overlap so that some data values, such as 20, fall within two classes. There is nothing wrong with using these class limits for the data set.
The classes overlap so that some data values, such as 20, fall within two classes.
Numbers are often assigned to data that are categorical in nature. (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. Yes, the data has an ordering to its categories. No, the data can be put into categories, but a comparison between values means nothing. No, the data has an ordering, the differences are important and we can find ratios between data values. Yes, this data can be put into categories and order doesn't matter. No, the data has an ordering, and the differences between data values are important. 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. Yes, the data has an ordering, and the differences between data values are important. Yes, the data has an ordering, the differences are important and we can find ratios between data values. No, while the data has an ordering to its categories, comparing them to each other is meaningless. No, while the data can be put into categories, order doesn't matter.
Yes, the data has an ordering to its categories. No, while the data has an ordering, and the data can be compared to each other, the differences don't mean anything.
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.) A placebo is used for the remaining 12 calves. After inoculation, test 5 calves to see if there is a difference in resistance to infection between the two groups. Use random selection to pick 5 calves to inoculate. After inoculation, test 10 calves to see if there is a difference in resistance to infection between the two groups. No placebo is being used. After inoculation, test all calves to see if there is a difference in resistance to infection between the two groups. Use random selection to pick 10 calves to inoculate.
a No placebo is being used. After inoculation, test all calves to see if there is a difference in resistance to infection between the two groups. Use random selection to pick 10 calves to inoculate.
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 stratified sample systematic sample cluster sample 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. simple random sample stratified sample systematic sample cluster sample 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. simple random sample stratified sample systematic sample cluster sample 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. simple random sample stratified sample systematic sample cluster sample 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. simple random sample stratified sample systematic sample cluster sample convenience sample
a simple random sample b cluster sample c convenience sample d systematic sample e stratified 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.) Students who are skipping class cannot be sampled. Home-schooled students cannot be sampled. Students who are on a school trip cannot be sampled. Students who are out sick cannot be sampled. Dropouts cannot be sampled. Students who are not taking statistics cannot be sampled. (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.) Home-schooled students cannot be sampled. Students who are out sick cannot be sampled. Students who are skipping class cannot be sampled. Dropouts cannot be sampled. Students who are on a school trip cannot be sampled.
a. Students who are skipping class cannot be sampled. Students who are on a school trip cannot be sampled. Students who are out sick cannot be sampled. b. Home-schooled students cannot be sampled. Dropouts cannot be sampled.
The book The Wall Street Journal. Guide to Information Graphics by Dona M. Wong gives strategies for using graphs and charts to display information effectively. One popular graph discussed is the donut pie chart. The donut pie chart is simply a pie chart with the center removed. A recent Harris Poll asked adults about their opinions regarding whether books should be banned from libraries because of social, language, violent, sexual, or religious content. The responses by education level to the question "Do you think that there are any books which should be banned completely?" are shown in the following donut pie charts. (a) What feature of Keith's graph makes it difficult to visually compare the responses of those with some college to those shown in the other graphs? (Select all that apply.) The graphs do not have data labels showing the percentages. The donut hole in the graph made by Keith is a different size than in the graphs made by Ramon. The graphs made by Keith and Ramon are all donut pie charts. The graphs made by Keith and Ramon compare groups across education level. The graphs made by Keith and Ramon use the same colors for each of the corresponding responses. b. How would you change Keith's graph for easier comparison? (Select all that apply.) Add data labels showing the percentages. Use different sets of colors in each of the donut pie charts. Make all donuts exactly the same size, with the radius of the holes the same as well. Change the graphs from donut pie charts to time series graphs. Combine the graphs into one donut pie chart. (c) Compare graphs made by Ramon. At which of the two education levels is the "no" response more frequent? High school or less Some college College graduate
a. The graphs do not have data labels showing the percentages. The donut hole in the graph made by Keith is a different size than in the graphs made by Ramon. b. Add data labels showing the percentages. Make all donuts exactly the same size, with the radius of the holes the same as well. c. College graduate
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 experiment because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured. This is an observational study because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured. 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. 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. (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 observational study because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured. This is an observational study because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured. 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. This is an experiment because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured. (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 observational study because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured. 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. 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. This is an experiment because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured. (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 experiment because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured. This is an observational study because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured. 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. 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.
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.
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 experiment simulation census (b) The effects of wind shear on airplanes during both landing and takeoff were studied by using complex computer programs that mimic actual flight. sampling experiment simulation census (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). sampling experiment simulation census (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). sampling experiment simulation census
a. sampling b. simulation c. census d. experiment
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. The patients do not know which treatment the other patients received. Neither the patients nor those administering the treatments know which patients received which treatments. The patients do not know which treatment they received. Those administering the treatments do not know which patients received which treatments. What are some benefits of such a procedure? (Select all that apply.) This process should eliminate potential bias from patient psychology regarding benefits of the drug. This process should eliminate potential bias from the patients' families. This process should eliminate potential bias from the researchers. This process should eliminate potential bias from the treatment administrators.
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.
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. nominal ordinal interval ratio (b) Price of company's stock nominal ordinal interval ratio (c) Names of new products nominal ordinal interval ratio (d) Temperature (°F) in CEO's private office nominal ordinal interval ratio (e) Gross income for each of the past 5 years nominal ordinal interval ratio (f) Color of product packaging nominal ordinal interval ratio
a. ordinal b. ratio c. nominal d. interval e. ratio f. nominal
Categorize these measurements associated with student life according to level: nominal, ordinal, interval, or ratio. (a)Length of time to complete an exam nominal ordinal interval ratio (b)Time of first class nominal ordinal interval ratio (c)Major field of study nominal ordinal interval ratio (d)Course evaluation scale: poor, acceptable, good nominal ordinal interval ratio (e)Score on last exam (based on 100 possible points) nominal ordinal interval ratio (f)Age of student nominal ordinal interval ratio
a. ratio b. interval c. nominal d. ordinal e. ratio f. ratio
(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.) No placebo is being used. Use random selection to pick nine schools to visit. A placebo is used for the remaining 9 schools. After the police visits, survey 9 of the schools to see if there is a difference in views between the two groups. After the police visits, survey all the schools to see if there is a difference in views between the two groups. Use random selection to pick 18 schools to visit.
b No placebo is being used. 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.
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, 4.6; rape, 27.4; robbery, 95.3; house burglary, 866.6; motor vehicle theft, 509.7; assault, 144.3. (a) Display this information in a Pareto chart, showing the crime rate for each category. (b) 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. No, the graph would be unable to account for all information. Yes, the graph would be able to account for all information. Yes, but the graph would take into account only these particular crimes and would not indicate if multiple crimes occurred during the same incident. Yes, but the graph would take into account only multiple crimes and not these particular individual crimes.
b Yes, but the graph would take into account only these particular crimes and would not indicate if multiple crimes occurred during the same incident.
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: 5852688672669789849191926668878673617075727385849057777684935847 (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? Sort of, these cowboys lived somewhat long lives, as evidenced by the high frequency of leaves for stems 5 and 6 (i.e., 50- and 60-year-olds). 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). No, these cowboys did not live long lives, as evidenced by the high frequency of leaves for stems 4 and 5 (i.e., 40- and 50-year-olds).
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).
(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.) No placebo is being used. A placebo patch is used for the remaining 35 volunteers in the second group. Use random selection to pick 35 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. Use random selection to pick 40 volunteers for the skin patch with the drug. Then record the smoking habits of the 40 volunteers to see if a difference exists between the two groups. Then record the smoking habits of the 35 volunteers to see if a difference exists between the two groups.
c. A placebo patch is used for the remaining 35 volunteers in the second group. Then record the smoking habits of all volunteers to see if a difference exists between the two groups. Use random selection to pick 40 volunteers for the skin patch with the drug.
A variable that consists of indivisible categories with no other scores existing between neighboring categories is called a(n) ______ variable. independent dependent discrete continuous
discrete
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. all cars miles per gallon new hybrid small cars total miles (b) Is the variable quantitative or qualitative? qualitative quantitative both quantitative and qualitative (c) What is the implied population? all cars all cars with average miles per gallon the new hybrid cars that were examined all new hybrid small cars
miles per gallon quantitative all new hybrid small cars
For a set population, does a parameter ever change? always unknown sometimes never 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 never vary from sample to sample, and so corresponding sample statistics may vary from sample to sample. Data from samples may vary from sample to sample, and so corresponding sample statistics may vary from sample to sample. Data from samples may vary from sample to sample, and so corresponding sample statistics never vary from sample to sample. Data from samples never vary from sample to sample, and so corresponding sample statistics never vary from sample to sample.
never Data from samples may vary from sample to sample, and so corresponding sample statistics may vary from sample to sample.
Using letter grades (A, B, C, D, and E) to classify student performance on an exam is an example of measurement on a(n) _______ scale of measurement. nominal ordinal interval ratio
ordinal
Although research questions usually concern a _________, the actual research is typically conducted with a ________. sample, statistic population, parameter sample, population population, sample
population, sample
Are data at the nominal level of measurement quantitative or qualitative? neither quantitative nor qualitative both quantitative and qualitative quantitative qualitative
qualitative
Determining a person's age (in years) would involve measurement on a(n) _____ scale of measurement. nominal ordinal interval ratio
ratio