Liberty University BUSI 230 week 1 exercises 1.1-2.1 complete solutions answers and more!

Liberty University BUSI 230 week 1 exercises 1.1-2.1 complete solutions answers and more!

Question 1

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

Question 2

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?

Question 3

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.

Question 4

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. 

What about at the interval level or higher? Explain. 

Question 5

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

Question 6

How long does it take to finish the 1161-mile Iditarod Dog Sled Race from Anchorage to Nome, Alaska? Finish times (to the nearest hour) for 57 dogsled teams are shown below.

261

271

236

244

279

296

284

299

288

288

247

256

338

360

341

333

261

266

287

296

313

311

307

307

299

303

277

283

304

305

288

290

288

289

297

299

332

330

309

328

307

328

285

291

295

298

306

315

310

318

318

320

333

321

323

324

327

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.)

Class Limits

Class Boundaries

Midpoint

Frequency

Relative 
Frequency

Cumulative 
Frequency

(c) Draw a histogram.

(d) Draw a relative-frequency histogram.

(e) Categorize the basic distribution shape.

(f) Draw an ogive. (Graph each point and the closed line segments connecting the points to create your graph.)

Question 7

Explain the difference between a stratified sample and a cluster sample. (Select all that apply.)

Question 8

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.)

Question 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.

(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.)

Question 10

What is the difference between a parameter and a statistic?

Question 11

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?

Question 12

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.

Question 13

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.

Question 14

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.

Question 15

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?

(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.

Question 16

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?

Question 17

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?

Question 18

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.

Question 19

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?

Question 20

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

Question 21

A data set with whole numbers has a low value of 20 and a high value of 89.

Find the class width for a frequency table with seven classes.

Find the class limits for a frequency table with seven classes.

Question 22

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. 

Question 23

How long does it take to finish the 1161-mile Iditarod Dog Sled Race from Anchorage to Nome, Alaska? Finish times (to the nearest hour) for 27 dogsled teams are shown below.

Make a dotplot for the data above regarding the finish time (number of hours) for the Iditarod Dog Sled Race. Select the appropriate dotplot below.

Compare the dotplot to a histogram of the data. (Select all that apply.)

Question 24

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).

(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 (USA Today).

(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).

Question 25

The Wind Mountain excavation site in New Mexico is an important archaeological location of the ancient Native American Anasazi culture. The following data represent depths (in cm) below surface grade at which significant artifacts were discovered at this site (Reference: A.I. Woosley and A.J. McIntyre, Mimbres Mogollon Archaeology, University of New Mexico Press).

For this problem, use seven 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 4 decimal places.)

(c) Draw a histogram.

(d) Draw a relative-frequency histogram.

(e) Categorize the basic distribution shape.

(f) Draw an ogive. (Graph each point and the closed line segments connecting the points to create your graph.)

Question 26

Another display technique that is somewhat similar to a histogram is a dotplot. In a dotplot, the data values are displayed along the horizontal axis. A dot is then plotted over each data value in the data set. For more details, view How to Make a Dotplot. The figure below shows a dotplot generated by Minitab for the number of licensed drivers per 1000 residents by state, including the District of Columbia (Source: U.S. Department of Transportation).

(a) From the dotplot, how many states have 600 or fewer licensed drivers per 1000 residents?

(b) About what percentage of the states (out of 51) seem to have close to 800 licensed drivers per 1000 residents? (Round your answer to one decimal place.)

(c) Consider the intervals 550 to 650, 650 to 750, and 750 to 850 licensed drivers per 1000 residents. In which interval do most of these states fall?

Question 27

What is the difference between a class boundary and a class limit? (Select all that apply.)

Question 28

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?