MAT 232 Week 2 Assignment Jennifer Sexton. practice questions and answers solved solution

Determine whether the data described below are qualitative or quantitative and explain why. The blood groups of A, B, AB, and O Choose the correct answer below. A. The data are qualitative because they don't measure or count anything. B. The data are qualitative because they consist of counts or measurements. C. The data are quantitative because they don't measure or count anything. D. The data are quantitative because they consist of counts or measurements. Determine whether the data described below are qualitative or quantitative and explain why. The television shows being watched by households surveyed by a media research company Choose the correct answer below. A. The data are qualitative because they consist of counts or measurements. B. The data are quantitative because they don't measure or count anything. C. The data are qualitative because they don't measure or count anything. D. The data are quantitative because they consist of counts or measurements. State whether the data described below are discrete or continuous, and explain why. The number of car accidents on a given stretch of highway each year Choose the correct answer below. A. The data are continuous because the data can only take on specific values. B. The data are discrete because the data can only take on specific values. C. The data are continuous because the data can take on any value in an interval. D. The data are discrete because the data can take on any value in an interval. State whether the data described below are discrete or continuous, and explain why. The lengths of carrots produced by a farm Choose the correct answer below. A. The data are continuous because the data can take on any value in an interval. B. The data are continuous because the data can only take on specific values. C. The data are discrete because the data can take on any value in an interval. D. The data are discrete because the data can only take on specific values. 1/16/2021 Week 2 - Assignment-Jennifer Sexton 5. 6. 7. 8. 9. For the data described below, identify the level of measurement as nominal, ordinal, interval, or ratio. The temperatures (in degrees Fahrenheit) that the thermostat is set to in different homes Choose the correct answer below. ratio ordinal interval nominal For the data described below, identify the level of measurement as nominal, ordinal, interval, or ratio. The sizes of coffee offered by a coffee shop (small, medium, large) Choose the correct answer below. nominal ratio ordinal interval Determine if the following statement represents a meaningful ratio, so the ratio level of measurement applies. A movie with a 4-star rating is twice as good as one with a 2-star rating. Choose the correct answer below. A. The ratio level of measurement does not apply. B. The ratio level of measurement applies. The temperatures (in °C) of air samples taken simultaneously over a large city are shown below. 20.5 18.8 21.4 19.8 19.5 20.4 18.3 18.9 18.6 Determine whether the data are qualitative or quantitative and identify the data set's level of measurement. Are the data qualitative or quantitative? Quantitative Qualitative What is the data set's level of measurement? Ordinal Ratio Interval Nominal One of the authors received a credit card bill for $ , but it included a charge of that was not valid. Find the values of the absolute and relative errors. 2,639 $1,701 The value of the absolute error is $ 1701 . The value of the relative error is 181 %. (Round to the nearest integer as needed) 1/16/2021 Week 2 - Assignment-Jennifer Sexton 10. Twenty-five people, consisting of a statistics professor and her students, are to measure the length of a room to the nearest tenth of a millimeter. Assume that everyone uses the same well-calibrated measuring device, such as a tape measure. Complete parts a through d below. a. All 25 measurements are not likely to be exactly the same; thus, the measurements will contain some sources of error. Are these errors systematic or random? Explain. A. These errors are random, because there is a tendency for the measurements to be all too high or too low. B. These errors are random. If they were systematic, there would be a tendency for the measurements to be all too high or all too low. C. These errors are systematic. If they were random, it would be undeterminable whether the measurements are all too high or too low. D. These errors are systematic, because it is undeterminable whether the measurements are too high or too low. b. If the professor wants to minimize the effect of random errors in determining the length of the room, is it better to report her own personal measurement as the length of the room or to report the average of all 25 measurements? Explain. A. It is better to use the average because it is likely to be in error by less than most of the individual measurements and it is more reliable than any single measurement. B. It is better to use the professor's own personal measurement because she has a more precise tape measure than her students. C. It is better to use the average because the average of many measurements is always equal to the true value. D. It is better to use the professor's own personal measurement because the random errors in the individual measurements will be multiplied in size 25 times in the average. c. Describe any possible sources of systematic errors in the measurement of the room length. A. Systematic errors might result if the students rush, and do not make the measurements carefully. B. Systematic errors might result if the tape measure has a manufacturing defect that made all of the units too small on the tape. C. Systematic errors might result if the tape measure is not long enough, and the students need to sum the measurements from the walls to some central point in the room. D. Systematic errors might result if there isn't much light in the room and the professor and students misread the tape measure. d. Can the process of averaging all 25 measurements help reduce any systematic errors? Why or why not? A. No, because measurements that have systematic errors cannot be averaged. B. Yes, because the average of many measurements is always equal to the true value. C. Yes, because the systematic errors will cancel out in the average. D. No, because if there is a systematic error in the measurements, that same error will be present in the average. 1/16/2021 Week 2 - Assignment-Jennifer Sexton 11. 12. 13. 14. 15. A new Corvette weighs pounds. A manufacturer's scale that is accurate to the nearest pound gives the weight as pounds, while the Department of Transportation uses a scale that is accurate to the nearest pound and obtains a weight of pounds. Which measurement is more precise? Which is more accurate? 3,272 0.1 3287.9 10 s 3280 Which measurement is more precise? Choose the correct answer below. A. The manufacturer's scale is more precise. B. The Department of Transportation scale is more precise. Which measurement is more accurate? Choose the correct answer below. A. The manufacturer's scale is more accurate. B. The Department of Transportation scale is more accurate. A study was conducted of pleas made by criminals. Among those criminals, pled guilty, and of them were sentenced to prison. Among the other criminals, who pled not guilty, were sent to prison. Complete (a) through (d). 1, 72 58 a. What percentage of the criminals pled guilty? 93 % (Round to the nearest tenth as needed.) b. What percentage of the criminals were sent to prison? 44 % (Round to the nearest tenth as needed.) c. Among those who pled guilty, what is the percentage who were sent to prison? 41.3 % (Round to the nearest tenth as needed.) d. Among those who pled not guilty, what is the percentage who were sent to prison? 80.6 % (Round to the nearest tenth as needed.) Last there were scheduled passenger flights in a certain country, and in of there were . Use a percentage to express the relative change. Use the second given value as the reference value. Also, write a statement describing the result. July 777,472 July 1995 759,191 The relative difference between July of 1995 and last July is 2 %. (Round to the nearest percent as needed.) There is a(n) % in the number of scheduled passenger flights from of to last . (Round to the nearest percent as needed.) 2 increase July 1995 July In a certain survey of adults, % reported having more than one television at home. Find the actual number of respondents corresponding to the given percentage. 1,043 83 The number of adults who reported having more than one television at home is 866 . (Round to the nearest integer as needed.) Fill in the blank in the following statement. If the population of state A is % less than the population of state B, then state A's population is _____% of state B's population. 20 If the population of state A is % less than the population of state B, then state A's population is % of state B's population. 20 80 1/16/2021 Week 2 - Assignment-Jennifer Sexton 16. 17. 18. If costs in the year are set equal to 100 so they can be used as the basis for determining index numbers, and the index number for the year 2012 is , what does a researcher know about costs in 2012 compared with costs in ? RAM memory 1998 28 RAM memory RAM memory 1998 Choose the correct answer below. A. The RAM memory costs in 2012 are 28% of those in the year 1998. B. The RAM memory costs in 1998 are 72% of those in the year 2012. C. The RAM memory costs in 2012 are 28% lower than those in the year 1998. D. The RAM memory costs in 1998 are 28% of those in the year 2012. E. The RAM memory costs in 2012 are 72% of those in the year 1998. F. The RAM memory costs in 2012 are 28% higher than those in the year 1998. In 1975 the price of gasoline per gallon was . With the 1975 price as the reference value, the gasoline price index for 1998 is . What was the cost of a gallon of gasoline in 1998? 55.9¢ 198.9 The cost of a gallon of gasoline in 1998 is $ 1.11 . (Round to the nearest cent as needed.) 1: Average Annual Consumer Price Index (=100) The typical (median) price of a single-family home in a certain region rose from $ in to $ in . Calculate the relative change in price from to , and compare it to the overall rate of inflation as measured by the Consumer Price Index. 73,,000 2007 Click the icon to view the Average Annual Consumer Price Index. 1 Home prices increased by 125 %. (Round to the nearest percent as needed.) The overall rate of inflation was 59 %. (Round to the nearest percent as needed.) Year CPI Year CPI Year CPI 1976 156...0 1977 160...6 1978 165...2 1979 172...1 1980 182...9 1981 190...0 1982 196...9 1983 199...3 1984 103...6 1985 107...3 1986 109...3 1/16/2021 Week 2 - Assignment-Jennifer Sexton 19. 20. 21. A frequency table of grades has five classes (A, B, C, D, F) with frequencies of , , , , and respectively. Using percentages, what are the relative frequencies of the five classes? 3 15 13 7 2 Complete the table. Grade Frequency Relative frequency A 3 7.5 % B 15 37.5 % C 13 32.5 % D 7 17.5 % F 2 5 % (Round to two decimal places as needed.) A frequency table of grades has five classes (A, B, C, D, and F) with frequencies of , , , , and respectively. What are the corresponding cumulative frequencies of the five classes? 2 11 15 4 3 Complete the table. Grade Frequency Cumulative frequency A 2 2 B 11 13 C 15 28 D 4 32 F 3 35 (Simplify your answers.) The following table shows grades for a term paper in an English class. The table is incomplete. Use the information given to fill in the missing entries and complete the table. Complete the table below. Category Frequency Relative frequency A 12 24 % B 8 16% C 14 28% D 12 24 % F 4 8 % Total 50 100 % (Simplify your answers.) 1/16/2021 Week 2 - Assignment-Jennifer Sexton 22. 2: Data Table A mathematician drilled a hole in a die, filled it with a lead weight, and then proceeded to roll it. The results are given in the following frequency table. Click the icon to view the frequency table. 2 a. According to the data, how many times was the die rolled? 200 (Simplify your answer.) b. How many times was the outcome greater than 2? 142 (Simplify your answer.) c. What percentage of outcomes were 6? 16 % (Type a whole number.) d. List the relative frequencies as decimals or integers, not percentages, that correspond to the given frequencies. Complete the table below. Outcome Relative frequency 1 .120 2 .170 3 .220 4 .185 5 .145 6 .160 (Type integers or decimals rounded to the nearest thousandth as needed.) e. List the cumulative frequencies that correspond to the given frequencies. Complete the table below. Outcome Cumulative frequency 1 24 2 58 3 102 4 139 5 168 6 200 (Simplify your answers.) Outcome Frequency 1 24 2 34 3 44 4 37 5 29 6 32 1/16/2021 Week 2 - Assignment-Jennifer Sexton 23. 24. The following histogram depicts cotinine levels (in milligrams per milliliter) of a sample of subjects who smoke cigarettes. Cotinine is a metabolite of nicotine, which means that cotinine is produced by the body when nicotine is absorbed. - 0 8 16 sample value Number of subjects 7 8 12 10 2 a. How many subjects are represented in the histogram? 39 (Simplify your answer.) b. How many subjects have cotinine levels below 400? 37 (Simplify your answer.) c. How many subjects have cotinine levels above 150? 24 (Simplify your answer.) d. What is the highest possible cotinine level of a subject represented in this histogram? 550 (Type a whole number.) 3: Data Table Use the following frequency table for the weights (in pounds) of cans of regular coke with bin width of 0.0050 pound to construct the corresponding histogram. 36 Click the icon to view the table. 3 Choose the correct graph below. A. 0.79 0.83 0 25 Weight Frequency B. 0.79 0.83 0 25 Weight Frequency C. 0.79 0.83 0 25 Weight Frequency D. 0.79 0.83 0 25 Weight Frequency Weight Frequency Relative frequency Cumulative frequency 0.7900 − 0.7949 2 2 / 36 2 0.7950 − 0.7999 0 0 2 0.8000 − 0.8049 2 2 / 36 4 0.8050 − 0.8099 3 3 / 36 7 0.8100 − 0.8149 4 4 / 36 11 0.8150 − 0. / 36 26 0.8200 − 0.8249 6 6 / 36 32 0.8250 − 0.8299 4 4 / 36 36 Total 36 1 36 Cotinine levels 1/16/2021 Week 2 - Assignment-Jennifer Sexton 25. A study was conducted to determine how people get jobs. The table lists data from 400 randomly selected subjects. Construct a Pareto chart that corresponds to the given data. If someone would like to get a job, what seems to be the most effective approach? Job Sources Frequency Help-wanted ads (H) 44 Executive search firms (E) 276 Networking (N) 25 Mass mailing (M) 55 Choose the correct Pareto chart. A. E M H N 0 50 100 150 200 250 300 B. E M H N 0 50 100 150 200 250 300 C. H E N M 0 50 100 150 200 250 300 D. H E N M 0 50 100 150 200 250 300 If someone would like to get a job, what seems to be the most effective approach? A. Networking (N) B. Executive search firms (E) C. Mass mailing (M) D. Help-wanted ads (H) 1/16/2021 Week 2 - Assignment-Jennifer Sexton 26. 4: Survey Results 5: Pareto Chart of Survey Results A survey was conducted to determine how employees found their jobs. The accompanying table and Pareto chart give the successful methods identified by 400 randomly selected employees. Construct a pie chart for these data. Compare the pie chart to the Pareto chart. Can you determine which graph is more effective in showing the relative importance of job sources? Click on the icon to view the survey results. 4 Click on the icon to view the Pareto chart. 5 Choose the correct pie chart below. A. 18% 12% 65% 6% B. 6% 65% 12% 18% C. 65% 6% 18% 12% D. 1% 10% 77% 12% Is the Pareto chart or the pie chart more effective in showing the relative importance of job sources? A. The pie chart is more effective in showing the relative importance of job sources, because Pareto charts should only be used with relative frequencies. B. The pie chart is more effective in showing the relative importance of job sources, because the wedges in a pie chart represent the relative frequencies while the bars in a Pareto chart are unrelated to the importance of job sources. C. The Pareto chart is more effective in showing the relative importance of job sources because the heights of the bars in the Pareto chart represent frequencies while the wedges in a pie chart are unrelated to the importance of job sources. D. The Pareto chart is more effective in showing the relative importance of job sources by using a vertical scale and arranging the bars in descending order. E. Neither chart is effective in showing the relative importance of job sources. Job sources of survey respondents Frequency Help-wanted ads 70 Executive search firms 48 Networking 260 Mass mailing 22 1/16/2021 Week 2 - Assignment-Jennifer Sexton 27. C A B D 0 50 100 150 200 250 300 Job Sources Frequency 6: Data Table A magazine article suggested that you can measure the ease of typing a word while using a particular keyboard configuration by using a certain rating system to assign points to each word. Using the rating system with a certain group of 26 words results in the rating values below. Use these values to construct a dotplot. Click the icon to view the rating values. 6 Choose the correct graph below. A. 0 12 0 15 Rating Frequency B. 0 12 0 15 Rating Frequency C. 0 12 0 15 Rating Frequency D. 0 12 0 15 Rating Frequency Qwerty keyboard word ratings 8 7 5 6 6 8 10 7 2 2 10 5 8 2 5 4 2 6 2 6 1 7 2 7 2 3 1/16/2021 Week 2 - Assignment-Jennifer Sexton 28. 29. The data table below shows the year-end price of gold (in dollars) over 14 consecutive years. Graph the data with a time-series plot. Year 1 2 3 4 5 6 7 8 9 10 Price($) Choose the correct time-series plot of the data. A. 1 14 100 600 Year Price ($) B. 1 14 100 600 Year Price ($) C. 1 14 100 600 Year Price ($) D. 1 14 100 600 Year Price ($) Construct a stem-and-leaf plot of the test scores How does the stem-and-leaf plot show the distribution of these data? 68, 72, 86, 75, 89, 89, 87, 90, 98, 100. Construct the stem-and-leaf plot. Choose the correct answer below. A. Stem Leaves 6 8 7 2 5 8 6 7 9 9 9 0 8 10 0 B. Stem Leaves 6 8 7 2 6 8 6 6 9 7 9 0 9 10 0 C. Stem Leaves 6 5 7 2 5 8 6 9 9 7 9 0 7 10 0 D. Stem Leaves 6 8 7 2 5 8 6 9 9 6 9 0 8 10 0 How does the stem-and-leaf plot show the distribution of these data? A. The lengths of the rows are similar to the heights of bars in a histogram; longer rows of data correspond to smaller frequencies. B. The lengths of the rows are similar to the widths of bars in a histogram; longer rows of data correspond to smaller frequencies. C. The lengths of the rows are similar to the heights of bars in a histogram; longer rows of data correspond to higher frequencies. D. The lengths of the rows are similar to the widths of bars in a histogram; longer rows of data correspond to higher frequencies. 1/16/2021 Week 2 - Assignment-Jennifer Sexton 30. The graph to the right depicts the marriage and divorce rates for selected years since 1900. Both rates are given in units of marriages/divorces per 1,000 people in the population. 0 2 4 6 8 10 12 14 Year Rates Marriage Divorce a. Why do these data consist of marriage and divorce rates rather than total numbers of marriages and divorces? A. Total numbers in both categories are constant, so the rates give better information about trends. B. Total numbers in either category may have increased or decreased due to an increasing or decreasing population, so the rates give better information about trends. C. Total numbers in both categories have gone down because of decreasing or increasing population, so the rates give better information about trends. b. Construct a stack plot of the marriage and divorce rate data. For each bar, place the divorce rate above the marriage rate. Choose the correct answer below. A. 0 3 6 9 12 15 18 Year Rates B. 0 3 6 9 12 15 18 Year Rates C. 0 3 6 9 12 15 18 Year Rates Which graph makes the comparisons easier: the multiple bar graph in the problem statement or the stack plot? A. The stacked plot makes comparison easier. The heights of the bars in the multiple bar graph aren't meaningful because the total number of marriages and divorces are more important values. B. By showing the years' bars side by side, the multiple bar graph makes comparison easier. The total heights of the bars in the stacked plot aren't meaningful. 1/16/2021 Week 2 - Assignment-Jennifer Sexton 31. The stacked line chart shows the numbers of college degrees awarded to men and women over time. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Year College graduates (hundred thousands) Men Women a. Estimate the numbers of college degrees awarded to men and to women (separately) in 1930 and in 1990. The number of college degrees awarded to men in 1930 was . The number of college degrees awarded to women in 1930 was . 75,000 50,000 The number of college degrees awarded to men in 1990 was . The number of college degrees awarded to women in 1990 was . 547,500 564,500 b. Compare the numbers of degrees awarded to men and to women (separately) in 1980 and 2000. Choose the correct answer below. A. In 1980, more women than men received degrees; in 2000, more men than women received degrees. B. In 1980 and in 2000, the number of men and women who received degrees were the same. C. In 1980, more men than women received degrees; in 2000, more women than men received degrees. c. During what decade did the total number of degrees awarded increase the most? A. 1960s B. 1920s C. 1940s D. 1990s d. Compare the total numbers of degrees awarded in 1950 and 2000. The total number of degrees awarded in 1950 was 450,000 . The total number of degrees awarded in 2000 was 1,174,000 . 1/16/2021 Week 2 - Assignment-Jennifer Sexton 32. When constructing a graph showing the population of two countries, an illustrator draws two different people with heights proportional to the populations. Identify a way in which the graph might be misleading. What is the general name for such graphs that use drawings of people or objects? How might the graph be misleading? A. The graph might be misleading because the illustrator draws too many people and the person who represents each country's population will be ambiguous. B. The graph might be misleading because the aspect of the drawings of people that represent the population of each country could be ambiguous. Viewers of the graph may interpret the area of each person as representing the respective populations. C. The graph might be misleading because the illustrator draws too few people. The illustrator should draw one person to represent each person in the countries. D. There is no way such a graph could be misleading. What is the general name for a graph that uses drawings of people or objects? A. A stemplot B. A pictograph C. A pie chart D. A stack plot E. A Pareto chart 1/16/2021 Week 2 - Assignment-Jennifer Sexton 33. 7: Fuel Consumption Data (mi/gal) The accompanying figure shows the highway fuel consumption (mi/gal) for two different models of car. How is the graph misleading? How could it be drawn so that it is not misleading? Click the icon to view the figure. 7 How is the graph misleading? A. The graph is misleading because it does not use a uniform scale for the vertical axis. B. The graph is misleading because the vertical axis scale does not start at zero. C. The graph is misleading because the height of each bar is proportional to the fuel consumption for the two cars, but the area of each bar is proportional to the square of each car's fuel consumption. D. The graph is misleading because the fuel consumption for each car is given in different units. How could the graph be drawn so that it is not misleading? A. By using a uniform scale on the vertical axis, the graph will not be misleading. B. By starting the vertical scale at 0, the graph will not be misleading. C. By keeping the width of each bar in the graph constant while their heights vary, the area of each bar will be proportional to the fuel consumption of each car and the graph will not be misleading. D. By giving the fuel consumption for each car in the same units, the graph will not be misleading. Car A Car B 40 45 50 x Highway fuel consumption (mi/gal) 1/16/2021 Week 2 - Assignment-Jennifer Sexton 34. 8: Graph/Chart The graph shows the percentage change in a price index over 17 years. In what year(s) (of the years displayed) was the change in the price index the greatest? In what year(s) was the change in the price index the least? How do actual prices in 1991 compare to those in 1990? Based on this graph, what can you conclude about changes in prices during the period shown? Click the icon to view the graph. 8 In what year(s) (of the years displayed) was the change in the price index the greatest? A. 2000 and 2005 B. 1992 C. 2002 D. 1990 In what year(s) was the change in the price index the least? A. 1995 B. 1998 and 2002 C. 1993 D. 1992, 1993, and 1996 How do actual prices in 1991 compare to those in 1990? A. The actual 1991 prices are about 4.2% less than those in 1990. B. The actual 1991 prices are about 4.2% higher than those in 1990. C. The actual 1991 prices are about 4.6% higher than those in 1990. D. The actual 1991 prices are about 4.6% less than those in 1990. Based on this graph, what can you conclude about changes in prices during the period shown? A. Prices have not increased in every year, but the increases near the end of the time period are lower than those near the beginning. B. Prices have increased in every year, but the increases near the end of the time period are lower than those near the beginning. C. Prices have increased in every year, but the increases near the end of the time period are larger than those near the beginning. 0 1 2 3 4 5 6 Percent change from previous year