Test 1 (ch. 1) Practice Questions

(1.1#9)Government agencies carefully monitor water quality and its effect on wetlands (Reference: Environmental Protection Agency Wetland Report EPA 832-R-93-005). 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)Is the variable quantitative or qualitative? (c)What is the implied population?

(a) Nitrogen concentration (mg nitrogen/L water). (b) Quantitative. (c) Nitrogen concentration (mg nitrogen/L water) in the entire lake.

(1.3#5)Zane is examining two studies involving how different generations classify specified items as either luxuries or necessities. In the first study, the Echo generation is defined to be people ages 18-29. The second study defined the Echo generation to be people ages 20-31. Zane notices that the first study was conducted in 2006 while the second one was conducted in 2008. (a)Are the two studies inconsistent in their description of the Echo generation? (b)What are the birth years of the Echo generation?

(a) No, those ages 18-29 in 2006 became ages 20-31 in 2008. (b) 1977-1988 (inclusive).

(1.1#5)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 useful-ness 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. What about at the interval level or higher? Explain.

(a) Nominal level. There is no apparent order relationship among responses. (b) Ordinal level. There is an increasing relationship from worst to best level of service. The interval between service levels is not meaningful, nor are ratios.

(1.1#13)Categorize these measurements associated with fishing according to level: nominal, ordinal, interval, or ratio. (a)Species of fish caught: perch, bass, pike, trout (b)Cost of rod and reel (c)Time of return home (d)Guidebook rating of fishing area: poor, fair, good (e)Number of fish caught (f)Temperature of water

(a) Nominal. (b) Ratio. (c) Interval. (d) Ordinal. (e) Ratio. (f ) Interval.

(1.3#7)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 heart worm, 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) Observational study. (b) Experiment. (c) Experiment. (d) Observational study

(1.1#11)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

(1.1#7)A national survey asked 1261 U.S. adult fast-food customers which meal (breakfast, lunch, dinner, snack) they ordered. (a)Identify the variable. (b)Is the variable quantitative or qualitative? (c)What is the implied population?

(a) Response regarding meal ordered at fast-food restaurants. (b) Qualitative. (c) Responses for all adult fast-food customers in the U.S.

(1.2#19)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, manu-facturing, 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.

(1.2#7)Greg took a random sample of size 100 from the popula-tion of current season ticket holders to State College men's basketball games. Then he took a random sample of size 100 from the population of current season ticket holders to State College women's basketball games. (a)What sampling technique (stratified, systematic, cluster, multistage, convenience, random) did Greg use to sample from the population of current season ticket holders to all State College basketball games played by either men or women? (b)Is it appropriate to pool the samples and claim to have a random sample of size 200 from the population of current season ticket holders to all State College home basketball games played by either men or women? Explain.

(a) Stratified. (b) No, because each pooled sample would have 100 season ticket holders for men's basketball games and 100 for women's basketball games. Samples with, say, 125 ticket holders for men's basketball games and 75 for women's games are not possible.

(1.3#9)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. (b)The Denver Police Department wants to improve its image with teenag-ers. 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. (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 1 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 2 months, each subject is surveyed regarding his or her current smoking habits.

(a) Use random selection to pick 10 calves to inoculate; test all calves; no placebo. (b) Use random selection to pick 9 schools to visit; survey all schools; no placebo. (c) Use random selection to pick 40 volunteers for skin patch with drug; survey all volunteers; placebo used

(1.1#3)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.

(1.1#1)In a statistical study what is the difference between an individual and a variable?

An individual is a member of the population of interest. A variable is an aspect of an individual subject or object being measured.

(1.3#1)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.

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

(1.1#15)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. (b)Do you think each student asked will allow you to weigh his or her backpack? (c)Do you think telling students ahead of time that you are going to weigh their backpacks will make a difference in the weights?

Answers vary. (a) For example: Use pounds. Round weights to the nearest pound. Since backpacks might weigh as much as 30 pounds, you might use a high-quality bathroom scale. (b) Some students may not allow you to weigh their backpacks for privacy reasons, etc. (c) Possibly. Some students may want to impress you with the heaviness of their backpacks, or they may be embarrassed about the "junk" they have stowed inside and thus may clean out their backpacks.

(1.2#11)Use a random-number table to generate a list of 10 random numbers between 1 and 99. Explain your work.

Answers vary. Use groups of two digits.

(1.3#11)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 exper-iment 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 gray region. Which blocking scheme, A or B, would be better? Explain. (LOOK AT TEST 1 PICTURE REFERENCE)

Based on the information given, Scheme A is best because it blocks all plots bordering the river together and all plots not bordering the river together. The blocks of Scheme B do not seem to differ from each other.

(1.2#1)Explain the difference between a stratified sample and a cluster sample.

In a stratified sample, random samples from each stratum 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.

(1.2#5)In a random sample of 50 students from a large university, all the students were between 18 and 20 years old. Can we conclude that the entire population of students at the university is between 18 and 20 years old? Explain.

No, even though the sample is random, some students younger than 18 or older than 20 may not have been included in the sample.

(1.3#3)A brief survey regarding opinions about recycling was carefully designed so that the wording of the questions would not influence the responses. Jill administered the survey at a farmer's market. She ap-proached adults and asked if they would fill out the survey, explaining that the results might be used to set trash collection and recycling policy in the city. She stood by silently while the form was filled out. Jill was wearing a green T-shirt with the slogan "fight global warming." Are the respondents a random sample of people in the community? Are there any concerns that Jill might have influenced the respondents?

No, respondents do not constitute a random sample from the community for several reasons; for instance, the sample frame includes only those at a farmer's market, Jill might not have approached people with large dogs or those who were busy, and participation was voluntary. Jill's T-shirt may have influenced respondents.

(1.2#13)Use a random-number table to generate a list of six random numbers from 1 to 8615. Explain your work.

Select a starting place in the table and group the digits in groups of four. Scan the table by rows and include the first six groups with numbers between 0001 and 8615

(1.2#17)Professor Gill is designing a multiple-choice test. There are to be 10 questions. Each question is to have five choices for answers. The choices are to be designated by the letters a, b, c, d, and e.Professor Gill wishes to use a random-number table to determine which letter choice should correspond to the correct answer for a question. Using the number correspondence 1 for a, 2 for b, 3 for c, 4 for d, and 5 for e, use a random-number table to determine the letter choice for the correct answer for each of the 10 questions.

Since there are five possible outcomes for each question, read single digits from a random-number table. Select a starting place and proceed until you have 10 digits from 1 to 5. Rep-etition is required. The correct answer for each question will be the letter choice corresponding to the digit chosen for that question.

(1.2#3)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 accounts only for the difference in results based on the use of a sample rather than of the entire population.

(1.2#9)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. Explain how you could get a random sample of four students from your statistics class. (a)Explain why the first four students walking into the classroom would not necessarily form a random sample. (b)Explain why four students coming in late would not necessarily form a random sample. (c)Explain why four students sitting in the back row would not necessarily form a random sample. (d)Explain why the four tallest students would not necessarily form a random sample.

Use a random-number table to select four distinct numbers corresponding to people in your class. (a) Reasons may vary. For instance, the first four students may make a special effort to get to class on time. (b) Reasons may vary. For instance, four stu-dents who come in late might all be nursing students enrolled in an anatomy and physiology class that meets the hour before in a faraway building. They may be more motivated than other students to complete a degree requirement. (c) Reasons may vary. For instance, four students sitting in the back row might be less inclined to participate in class discussions. (d) Reasons may vary. For instance, the tallest students might all be male.