DS 265 Ch 1-3 Study guide

Find the z-score for an IQ test score of 125 when the mean is 100 and the standard deviation is 15. Multiple Choice −1.1 1.67 1.1 25 −1.67 (Chapter 3)

1.67 Explanation Z-score = (x − mean)/std dev = (125 − 100)/15 = 25/15 = 1.67

The company financial officer was interested in the average cost of PCs that had been purchased in the past six months. She took a random sample of the price of 10 computers, with the following results.$3,250, $1,127, $2,995, $3,250, $3,445, $3,449, $1,482, $6,120, $3,009, $4,000What is the 65th percentile? Multiple Choice $3,445.00 $4,212.00 $3,587.00 $2,617.00 $1,446.50 (Chapter 3)

$3,445.00 Explanation Place scores in ascending order and calculate the index = (p/100)n = (65/100) × 10 = 6.5. When the index is not an integer, round up to the next integer to obtain the index value: 6.5 rounds to 7; the seventh value is 3445.

Consider the frequency distribution of exam scores given below. Class Frequency 50 < 60 6 60 < 70 15 70 < 80 19 80 < 90 6 90 < 100 4 (a & b) Fill in the following table. (c) Choose a percent frequency polygon. Graph AGraph BGraph C multiple choice 1Graph A CorrectGraph BGraph C (d) Choose a percent frequency ogive. Frequency ogive AFrequency ogive BFrequency ogive C multiple choice 2Frequency ogive A CorrectFrequency ogive BFrequency ogive C rev: 05_15_2019_QC_CS-168749, 01_25_2022_QC_CS-292890 Explanation (a & b)Frequency Distribution for Exam Scores LowerUpperMidpointWidthFrequencyPercentRelative FrequencyCumulative FrequencyCumulative Percent506055106120.126126070651015300.3021427080751019380.384080809085106120.124692901009510480.0850100 (Chapter 2)

(A & B): Classs Frequency Cumulative Frequency Cumulative % Frequency 50 < 60 6 6 12% 12% 60 < 70 15 21 30% 42% 70 < 80 19 40 38% 80% 80 < 90 6 46 12% 92% 90 < 100 4 50 8% 100% (C):Graph A (D):Frequency ogive A Explanation (a & b)Frequency Distribution for Exam Scores LowerUpperMidpointWidthFrequencyPercentRelative FrequencyCumulative FrequencyCumulative Percent506055106120.126126070651015300.3021427080751019380.384080809085106120.124692901009510480.0850100

Suppose that a company's sales were $5,000,000 three years ago. Since that time sales have grown at annual rates of 10 percent, -10 percent, and 25 percent. (a) Find the geometric mean growth rate of sales over this three-year period. (Round your answer to 2 decimal places.) (b) Find the ending value of sales after this three-year period. (Do not round intermediate calculations and round your final answer to nearest dollar amount.) (Chapter 3)

(A) 7.36% (B) Ending value:6,187,500 Explanation (a) Rg =(1+ .1) (1−.1) (1+.25)−−−−−−−−−−−−−−−−−−−−√3 −1=1.0736−1=.0736=7.36% Rg⁢ =(1+ .1) (1−.1) (1+.25)3⁢ −1=1.0736−1=.0736⁢=7.36% (b) I(1 + Rg)n = $5,000,000(1 + .0736)3 = $6,187,500

Consider three stock funds, which we will call Stock Funds 1, 2, and 3. Suppose that Stock Fund 1 has a mean yearly return of 5.20 percent with a standard deviation of 17.80 percent; Stock Fund 2 has a mean yearly return of 21.20 percent with a standard deviation of 15.00 percent, and Stock Fund 3 has a mean yearly return of 9.00 percent with a standard deviation of 4.20 percent. (a) For each fund, find an interval in which you would expect 95.44 percent of all yearly returns to fall. Assume returns are normally distributed. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.) (b) Using the intervals you computed in part a, compare the three funds with respect to average yearly returns and with respect to variability of returns. (c) Calculate the coefficient of variation for each fund, and use your results to compare the funds with respect to risk. Which fund is riskiest? (Round your answers to 2 decimal places.) (Chapter 3)

(A): Fund 1: [(30.40),40.80] Fund 2: [(8.80),51.20] Fund 3: [0.60,17.40] (B): Fund 1 has the lowest average return and the highest variability Fund 2 has the highest average return and the middle variability Fund 1 has the middle average return and the smallest variability (C): Fund 1: Coefficient of Variation = 17.80 / 5.20 * 100 = 342.31% Fund 2: Coefficient of Variation = 15.00 / 21.20 * 100 = 70.75% Fund 3: Coefficient of Variation = 4.20 / 9.00 * 100 = 46.67% Fund 1 is riskiest, Fund 2 is second riskiest and Fund 3 is least risky Explanation (a) Fund 1: [5.20 - 2*17.80, 5.20 + 2*17.80] = [−30.40, 40.80] Fund 2: [21.20 - 2*15.00, 21.20 + 2*15.00] = [−8.80, 51.20] Fund 3: [9.00 - 2*4.20, 9.00 + 2*4.20] = [.60, 17.40] (c) Fund 1: Coefficient of Variation = 17.80 / 5.20 * 100 = 342.31% Fund 2: Coefficient of Variation = 15.00 / 21.20 * 100 = 70.75% Fund 3: Coefficient of Variation = 4.20 / 9.00 * 100 = 46.67%

The following frequency distribution summarizes the weights of 195 fish caught by anglers participating in a professional bass fishing tournament. Weight (Pounds) Frequency 1-3 5 4-6 120 7-9 35 10-12 35 (a) Calculate the (approximate) sample mean for these data. (Round your answer to 2 decimal places.) (b) Calculate the (approximate) sample variance for these data. (Chapter 3)

(A): 6.54 lbs (B) 5.971 Explanation Weight Frequency (fi)Midpoint (Mi)fi Mi Mi − x¯x¯(Mi − x¯x¯ )2fi(Mi − x¯x¯ )21 - 35210−4.5420.6116103.064 - 61205600−1.542.3716284.597 - 93582801.462.131674.6110 - 1235113854.4619.8916696.21 195 1,275 1,158.46 (a) Approximate x¯=ΣfiMin=1,275195=6.54 Approximate x¯=ΣfiMin=1,275195=6.54 (b) Approximate s2=Σfi(Mi−x¯)2n−1=1,158.46194=5.971

Calculate the mean, median, and mode of each of the following populations of numbers: (Round your mean and median value to 1 decimal place.) (a) 9, 4, 14, 12, 8, 12, 14, 4, 4, 11 N (Population)____, Mean____, Median____, Mode____ (b) 97, 122, 105, 83, 125, 92, 97, 115, 82 N (Population)____, Mean____, Median____, Mode____ (Chapter 3)

(A)N (Population) 10, Mean 9.2, Median 10.0, Mode 4 (B)N (Population) 9, Mean 102.0, Median 97.0, Mode 97 Explanation (a) N = 10, Mean = 9.2, Median = 10.0, Mode = 4 (b) N = 9, Mean = 102.0, Median = 97.0, Mode = 97

The following is a partial relative frequency distribution of consumer preferences for four products—W, X, Y, and Z. Partial Relative Frequency Distribution Table Product Relative Frequency W 0.19X X - Y 0.11 Z 0.15 (a) Find the relative frequency for product X. (Round your answer to 2 decimal places.) (b) If 1,000 consumers were surveyed, give the frequency distribution for these data. Frequency Distribution Table Product Frequency W - X - Y - Z - (d) If we wish to depict these data using a pie chart, find how many degrees (out of 360) should be assigned to each of products W, X, Y, and Z. (Round your answers to 1 decimal place.) Product Degrees W - X - Y - Z - (Chapter 2)

(A)Relative Frequency:0.55 (B)Frequency Distribution Table Product Frequency W 190 X 550 Y 110 Z 150 (D) Product Degrees W 68.4 X 198.0 Y 39.6 Z 54.0 Explanation (a) Relative frequency for product × is 1 - (0.19 + 0.11 + 0.15) = 0.55 (b)Frequency and Relative Frequency Table for Products W, X, Y, Z Product Relative Frequency Frequency =n × Relative frequency W 0.19 1,000 × 0.19 = 190 X 0.55 1,000 × 0.55 = 550 Y 0.11 1,000 × 0.11 = 110 Z 0.15 1,000 × 0.15 = 150 (d)Calculation for Degrees for Pie Chart of Product Frequencies Product Relative Frequency Degrees =360 × Relative Frequency W 0.19 360 × 0.19 = 68.4 X 0.55 360 × 0.55 = 198.0 Y 0.11 360 × 0.11 = 39.6 Z 0.15 360 × 0.15 = 54.0

In a study of the factors that affect success in economics, data were collected for 8 business students. Scores on a calculus placement test are given with economics final exam scores. The data are below. Calculus Placement Score Exam Final Score 17 73 21 66 11 64 16 61 15 70 11 71 24 90 27 68 It can be shown that for these data: X ¯¯¯¯¯ =17.75; y¯ = 70.38; ∑8i=1 (xi − x¯)2 = 237.50; ∑8i=1 (yi − y¯)2 = 545.875; ∑8i=1 (xi − x¯)(yi − y¯) = 140.75.X ¯ =17.75; y¯ = 70.38; ∑i=18 (xi - x¯)2 = 237.50; ∑i=18 (yi - y¯)2 = 545.875; ∑i=18 (xi - x¯)(yi - y¯) = 140.75. Calculate b1. Multiple Choice .26 −.59 −.26 .59 .15 (Chapter 3)

.59 Explanation r = Sxy /(Sx × Sy) = 20.11/51.44 = .39

Suppose that a company's sales were $1,000,000 four years ago and are $7,000,000 at the end of the four years. Find the geometric mean growth rate of sales. (Round your answer to 4 decimal places.) (Chapter 3)

0.6266 Explanation 1,000,000(1 + Rg)4 = 7,000,000 (1 + Rg)4 = 7 (1 + Rg) = 7-√474 Rg = 1.6266 - 1 Rg = 0.6266

The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes; mean = 114.15):118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118.What is the range? Multiple Choice 557.97 115 23.62 128.8 103 (Chapter 3)

103 Explanation Range = largest value − smallest value = 148 − 45 = 103

The following is a relative frequency distribution of grades in an introductory statistics course. Grade Relative Frequency A 0.22 B ? C 0.18 D 0.17 F 0.06 If this was the distribution of 200 students, find the frequency for the highest two grades. Multiple Choice 44 35 118 59 74 (Chapter 2)

118 Explanation (.22 + .37) = .59. 59% of 200 = 118.

A company's Chief Operating Officer (COO) keeps track of the mileage on her trips from her office at corporate headquarters to the company's off-site manufacturing facility and its nearby suppliers. The stem-and-leaf display of the data for one year is below. 76 9 77 114 78 79 07 80 88 81 2 82 1 83 88 7 12 11 10 9 (Chapter 2)

12 Explanation Count of measurements is 12.

According to Chebyshev's theorem, a range of how many standard deviations would include at least 80 percent of the values? 5.0 2.2 1.6 2.0 2.5 (Chapter 3)

2.2 Explanation 100(1 − 1 /k2)% = 100(1 − 1 /2.22)% = 80%

Find the z-score for an IQ test score of 142 when the mean is 100 and the standard deviation is 15. Multiple Choice 18.78 2.8 42 1.27 −2.8 (Chapter 3)

2.8 Explanation Z-score = (x − mean)/std dev = (142 − 100)/15 = 42/15 = 2.8

The number of weekly sales calls by a sample of 25 pharmaceutical salespersons is below.24, 56, 43, 35, 37, 27, 29, 44, 34, 28, 33, 28, 46, 31, 38, 41, 48, 38, 27, 29, 37, 33, 31, 40, 50How many classes should be used in the construction of a histogram? 6 2 4 10 5 (Chapter 2)

5 Classes are determined by the value of k, where 2k yields a value that is closest to the sample size and is also larger than the sample size. k = 5, so 25 = 32.

If there are 130 values in a data set, how many classes should be created for a frequency histogram? 6 7 8 5 4 (Chapter 2)

8 Explanation 2k, where k = number of classes and 2k is the closest value larger than 130. 27 = 128; 28 = 256.

A ________ displays the frequency of each class with qualitative data and a ________ displays the frequency of each class with quantitative data. stem-and-leaf, pie chart scatter plot, bar chart bar chart, histogram Correct histogram, stem-and-leaf display (Chapter 2)

Bar chart, Histogram Explanation The histogram and stem-and-leaf are used to graphically display quantitative data; a scatter plot is used for displaying the relationship between two variables.

As a business owner, I have requested my staff to develop a set of dashboards that can be used by the public to show wait time at each of my four local coffee shops at peak times during the day and whether the time is short, medium, or long. Which of the following graphical displays would be the best choice? sparkline gauges treemap bullet graph (Chapter 2)

Bullet graph Explanation A bullet graph is used when you are analyzing a single measure - in this case wait time.

Explain the difference between a census and a sample. (Chapter 1)

Census: examine all of the population units. Sample: subset of the units in a population.

In the treemap in Figure 2.41, dark blue represents the lowest ozone level and bright red represents the highest ozone level. Where is the ozone level higher - Chicago or New York City? (Chapter 2)

Chicago Explanation The ozone level is higher in Chicago because the corresponding rectangle is more nearly red.

Which of the following is a measure of the strength of the linear relationship between x and y that is dependent on the units in which x and y are measured? covariance Correct least squares line correlation coefficient slope (Chapter 3)

Covariance Explanation This tells you how close the relationship is to a straight line between x and y.

A stem-and-leaf display is best used to ________. display the shape of the distribution provide a point estimate of the central tendency of the data set display a two-variable treemap. provide a point estimate of the variability of the data set (Chapter 2)

Display the shape of the distribution Explanation It is more difficult to find central tendency and variability using a stem-and-leaf display. It is easy to visualize the shape of the distribution using stem-and-leaf.

A sample of 100 bank customer waiting times are given in the following table: Waiting Times (in Minutes) for the Bank Customer Waiting Time Case 6.7 7.6 8.54.911.611.010.6 7.8 7.26.27.05.47.97.2 5.1 .04.06.94.07.68.2 11.9 4.55.05.65.49.72.3 6.7 6.86.96.14.37.41.2 3.1 1.34.25.56.29.42.3 2.5 2.56.26.95.27.63.0 2.5 4.54.85.95.88.62.7 6.9 2.14.74.44.48.32.9 2.0 8.86.46.66.49.1.4 3.7 .86.44.45.110.2 6.8 8.57.06.66.17.2 3.4 5.74.66.15.18.4 5.7 10.26.34.86.410.9 2.6 4.45.44.88.69.4 A sample of 100 bank customer waiting times are given in the following table: The mean and the standard deviation of the sample of 100 bank customer waiting times are x¯x¯ = 5.889 and s = 2.536. (a) What does the histogram in Figure 2.16 say about whether the Empirical Rule should be used to describe the bank customer waiting times? (b) Use the Empirical Rule to calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all possible bank customer waiting times. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) (c) Does the estimate of a tolerance interval containing 68.26 percent of all waiting times provide evidence that at least two-thirds of all customers will have to wait less than 9 minutes for service? (d) How do the percentages of the 100 waiting times that actually fall into the intervals [ x¯x¯ ± s], [ x¯x¯ ± 2s], and [ x¯x¯ ± 3s] compare to those given by the Empirical Rule? Do these comparisons indicate that the statistical inferences you made in parts b and c are reasonably valid? (Round your answers to the nearest whole number.) (Chapter 3)

Explanation (a) It is somewhat reasonable because the distribution is approximately symmetric. (b) [ x¯x¯ ± s] = [5.889 ± 2.536] = [3.353,8.425] [ x¯x¯ ± 2s] = [5.889 ± 2(2.536)] = [.817,10.961] [ x¯x¯ ± 3s] = [5.889 ± 3(2.536)] = [-1.719,13.497] (c) Because the upper limit of the 68.26% interval is less than 9, there is strong evidence that at least ⅔ of the customers will wait less than 9 minutes. (d) 67 out of 100 (67%) actually fall into the interval x¯x¯ ± s. 94 out of 100 (94%) actually fall into the interval x¯x¯ ± 2s. 100 out of 100 (100%) actually fall into the interval x¯x¯ ± 3s. Since these percentages compare favorably with the values (68.26%, 95.44%, and 99.73%) given by the Empirical Rule, it suggests that our inferences are reasonably valid. (A): it Is somewhat reasonable (B): [x(bar)+-s] [3.353,8.425] [x(bar)+-2s] [0.8178,10.961] [x(bar)+-3s] [(1.719,13,297] (C):Yes, because the upper limit of the 68.26% interval is less than 9 minutes (D): 67% fall into [x(bar)+-s], 94% fall into [x(bar)+-2s], 100% fall into [x(bar)+-3s]. Yes, they are reasonably valid

A multiple choice question on an exam has four possible responses—(A), (B), (C), and (D). When 500 students take the exam, 100 give response (A), 100 give response (B), 100 give response (C), and 200 give response (D). Write out the frequency distribution, relative frequency distribution, and percent frequency distribution for these responses. (Round your relative frequency answers to 2 decimal places.) Frequency Distributions for Student Responses Category / Class Frequency Relative Frequency Percent Frequency A100 0.2020% B100 0.20 20% C 100 0.20 20% D 200 0.40 40% (Chapter 2)

Explanation Frequency, Relative Frequency, and Percent Frequency Table for Question Response Category /Class Frequency Relative Frequency Percent Frequency A 100 0.20 20% B 100 0.20 20% C 100 0.20 20% D 200 0.40 40%

A scatter plot is mainly used to identify outliers. True or False? (Chapter 2)

FALSE Explanation A scatter plot is used to identify the relationship between two variables.

When data are qualitative, the bars should never be separated by gaps. True or False? (Chapter 2)

FALSE Explanation Bar graphs for qualitative data are displayed with a gap between each category.

The term big data refers to the use of survey data by big business. True or False? (Chapter 1)

FALSE Explanation Big data is a term that arose from the huge capacity of data warehouses that contain massive amounts of data.

In an experimental study, the aim is to manipulate or set the value of the response variable. True or False? (Chapter 1)

FALSE Explanation In experimental studies, the aim is to manipulate the factor(s), which may be related to the response variable.

A quantitative variable can also be referred to as a categorical variable. True or False? (Chapter 1)

FALSE Explanation Qualitative variables are also known as categorical variables.

It is appropriate to use the Empirical Rule to describe a population that is extremely skewed. True or False? (Chapter 3)

FALSE Explanation The Empirical Rule should be used for normally distributed populations.

The geometric mean is the rate of change that yields better wealth at the end of a set of time periods than the actual returns. True or False? (Chapter 3)

FALSE Explanation The definition of geometric mean is the rate of change that yields the same wealth at the end of several time periods as do actual returns.

The line that minimizes the sum of the squared horizontal (x) distances between the points on the scatter plot and the line is the least squares line. True or False? (Chapter 3)

FALSE Explanation The definition of the least squares line is the line that minimizes the sum of the squared vertical distances (y) between the points.

The median is the measure of central tendency that divides a population or sample into four equal parts. True or False? (Chapter 3)

FALSE Explanation The median divides a population into two equal parts.

The range of the measurement is the largest measurement plus the smallest measurement. True or False? (Chapter 3)

FALSE Explanation The range is the largest minus the smallest measurement.

The population mean is the point estimate of the sample mean. True or False? (Chapter 3)

FALSE Explanation The sample mean is the point estimate of the population mean

An example of a quantitative variable is the manufacturer of a car. True or False? (Chapter 1)

FALSE Explanation This is an example of a qualitative or categorical variable.

An example of a qualitative variable is the mileage of a car. True or False? (Chapter 1)

FALSE Explanation This is an example of a quantitative variable.

The number of sick days taken by employees in 2008 for the top 10 technology companies is an example of time series data. True or False? (Chapter 1)

FALSE Explanation This is an example of cross-sectional data. Time series data are collected at different time periods.

Time series data are data collected at the same time period. True or False? (Chapter 1)

FALSE Explanation Time series data are collected over different time periods.

When we wish to summarize the proportion (or fraction) of items in a class, we use the frequency distribution for each class. True or False? (Chapter 2)

False Explanation The relative frequency summarizes the proportion (or fraction) of items in a class. Frequency distribution shows actual counts of items in each class.

A person's telephone area code is an example of a(n) ________ variable.: ratio nominative Correct interval ordinal (Chapter 1)

Nominative Explanation This is a qualitative variable without order; therefore, a nominative variable.

Which of the following divides quantitative measurements into classes and graphs the frequency, relative frequency, or percentage frequency for each class? histogram Correct dot plot scatter plot stem-and-leaf display (Chapter 2)

Histogram Explanation A box plot does not easily group measurements into classes; a scatter plot is for looking at the relationship between two variables.

If a data set consists of 1,000 measurements, would you summarize the data set using a histogram or a dot plot? Dot plot Histogram (Chapter 2)

Histogram Explanation With 1000 measurements it would not be practical to use a dot plot because of the number of dots.

When developing a frequency distribution, the class (group) intervals must be ________. equal nonoverlapping Correct large small integer (Chapter 2)

Nonoverlapping Explanation There is no definitive size of intervals for classes, and intervals can be fractional. The number of classes can result in the final class having a different interval size than the previous ones.

Jersey numbers of soccer players is an example of a(n) ________ variable. ordinal nominative Correct interval ratio (Chapter 1)

Nominative Explanation Interval and ratio are quantitative variables; jersey numbers have no logical order.

Measurements from a population are called: processes. variables. elements. observations. (Chapter 1)

Observations. Explanation By definition, elements are the members of the population and variables are characteristics of elements; a measurement (or observation) assigns a value to a variable for an element of the population. A process is a sequence of operations that takes inputs and turns them into outputs.

On its website, the Statesman Journal newspaper (Salem, Oregon, 2005) reports mortgage loan interest rates for 30-year and 15-year fixed-rate mortgage loans for a number of Willamette Valley lending institutions. Of interest is whether there is any systematic difference between 30-year rates and 15-year rates (expressed as annual percentage rate or APR) and, if there is, what is the size of that difference. The following table displays the 30-year rate and the 15-year rate for each of nine lending institutions. Also given is the difference between the 30-year rate and the 15-year rate for each lending institution. Use the table to compare the 30-year rates and the 15-year rates. Also, calculate the average of the differences between the rates. (Input the amount as positive value. Round your answer to 4 decimal places.) Lending Institution30-Year15-YearDifferenceBlue Ribbon Home Mortgage6.2044.0182.186Coast To Coast Mortgage Lending3.2192.5080.711Community Mortgage Services Inc.3.3343.629-0.295Liberty Mortgage3.5733.4850.088Jim Morrison's MBI4.5353.0341.501Professional Valley Mortgage5.7092.8202.889Mortgage First4.8683.7021.166Professional Mortgage Corporation6.2353.8152.420Resident Lending Group Inc.4.8313.2311.600 Overall, the 30-year rates are____the 15-year rates.The variability is____Average of the differences _____ (Chapter 3)

Overall, the 30 year rates are higher than the 15 year rates. The variability is larger. Average of the differences =1.3629

Figure 2.21 gives stem-and-leaf displays of the payment times in Table 2.4 and of the bottle design ratings in Table 1.6. Describe the shapes of two displays. Payment times distribution is Bottle design ratings distribution is (Chapter 2)

Payment times distribution is slightly skewed to the right Bottle design ratings distribution is slightly skewed to the left Explanation The Payment Times distribution is skewed to the right. The Bottle Design Ratings distribution is skewed to the left.

The change in the daily price of a stock is what type of variable? random quantitative Correct ordinal qualitative (Chapter 1)

Quantitative Explanation Qualitative and ordinal have similar definitions; random variables are all characteristics of a population element.

Which of the following is not a graphical tool for descriptive analytics (dashboards)? sparkline bullet graph raw data Correct gauge treemap (Chapter 2)

Raw data Explanation Raw data is data that has not been processed; no graphical tools have been applied to it yet.

________ is the difference between a numerical descriptor of the population and the corresponding descriptor of the sample.: Observation error Nonobservation error Nonresponse Sampling error (Chapter 1)

Sampling error Explanation Nonresponse, nonobservation and observation error occur during the survey process. Sampling error is a result of the survey process.

A plot that allows us to visualize the relationship between two variables is a(n) ________ plot. scatter Correct dot ogive frequency (Chapter 2)

Scatter Plot Explanation Scatter plots display the relationship between two variables.

A histogram that has a longer tail extending toward smaller values is ________. skewed to the left skewed to the right normal a scatter plot (Chapter 2)

Skewed to the left Explanation Smaller values are to the left of the center part of the graph, resulting in a tail to the left. Thus, the graph is skewed to the left.

A histogram that has a longer tail extending toward larger values is ________. skewed to the right Correct normal a scatter plot skewed to the left (Chapter 2)

Skewed to the right Explanation Larger values are to the right of the center part of the graph, resulting in a tail to the right. Thus, the graph is skewed to the right.

Classify each of the following qualitative variables as ordinal or nominative. Qualitative Variable Categories Statistics course letter grade A B C D F Door choice on Let's Make A Deal Door #1 Door #2 Door #3 Television show classifications TV-G TV-PG TV-14 TV-MA Personal computer ownership Yes No Restaurant rating ***** **** *** ** * Income tax filing status Married filing jointly; Married filing separately; Single; Head of household; Qualifying widow(er) (Chapter 1)

Statistics course letter grade: Ordinal A B C D F: Ordinal Door choice on Let's Make A Deal: Nominative Door #1 Door #2 Door #3: Nominative Television show classifications: Ordinal TV-G TV-PG TV-14 TV-MA: Ordinal Personal computer ownership: Nominative Yes No: Nominative Restaurant rating: Ordinal ***** **** *** ** *: Ordinal Income tax filing status: Nominative Married filing jointly; Married filing separately; Single; Head of household; Qualifying widow(er): Nominative Explanation Letter Grades: Ordinal - each grade from A to F indicates an increasingly lower grade. Door Choices: Nominative - each door is the same except for the number given. For example, Door 1 is not better or worse or higher or lower than Door 3. TV Classifications: Ordinal - each category from TV-G to TV-MA indicates programming appropriate for increasingly older viewers. PC Ownership: Nominative - no ordering of categories. Restaurant Ratings: Ordinal - each rating from 5-star to 1-star indicates an increasingly lower rating. Filing Status: Nominative - no ordering of categories.

A bar chart is a graphic that can be used to depict qualitative data. True or False? (Chapter 2)

TRUE Explanation A bar chart is a graphic that depicts a frequency, relative frequency, or percent frequency distribution.

A population is a set that includes all elements about which we wish to draw a conclusion. True or False? (Chapter 1)

TRUE Explanation A data set provides information about some group of individual elements, which may be people, object, events, or other entities.

A runs plot is a form of scatter plot. True or False? (Chapter 2)

TRUE Explanation A runs plot is also known as a times series plot.

Cross-sectional data are data collected at the same or approximately the same point in time. True or False? (Chapter 1)

TRUE Explanation Cross-sectional data are collected at the same point in time an example would be a specific month for a cell phone bill for several employees or sales during a specific time period.

Data warehousing is defined as a process of centralized data management and retrieval. True or False? (Chapter 1)

TRUE Explanation Data warehousing has as its centralized ideal the creation and maintenance of a central repository for all of an organization's data.

The stem-and-leaf display is advantageous because it allows us to actually see the measurements in the data set. True or False? (Chapter 2)

TRUE Explanation It visually displays all of the data points that were collected for an analysis.

A random sample is selected so that every element in the population has the same chance of being included in the sample. True or False? (Chapter 1)

TRUE Explanation On each random selection, we give every element in the population the same chance of being chosen.

In a symmetric population, the median equals the mode. True or False? (Chapter 3)

TRUE Explanation The population is a perfect bell curve.

In systematic sampling, the first element is randomly selected from the first (N/n) elements. True or False? (Chapter 1)

TRUE Explanation This is when you want to systematically select a sample of n elements without replacement from a frame of N elements.

A stem-and-leaf display is a graphical portrayal of a data set that shows the data set's overall pattern of variation. True or False? (Chapter 2)

TRUE Explanation This kind of graph places the measurements in order from smallest to largest.

When looking at the shape of the distribution using a histogram, a distribution is skewed to the right when the left tail is shorter than the right tail. True or False? (Chapter 2)

TRUE Explanation This type of histogram has a high frequency number of data points on the right compared to the left side of the histogram.

In an observational study, the variable of interest is called a response variable. True or False? (Chapter 1)

TRUE Explanation When initiating a study, we first define our variable of interest, or response variable. Other variables are called factors.

________ occurs when some population elements are excluded from the process of selecting the sample. Undercoverage Correct Nonresponse Error of observation Sample frame (Chapter 1)

Undercoverage Explanation Exclusion of population elements in selection is not a result of nonresponse or error of observation because this occurs during the survey itself. Sampling error is a result of the survey process.

Any characteristic of an element is called a ________. set census process variable (Chapter 1)

Variable Explanation A process is a sequence of operations; a census looks at the entire population; set is related to population.

According to a survey of the top 10 employers in a major city in the Midwest, a worker spends an average of 413 minutes a day on the job. Suppose the standard deviation is 26.8 minutes and the time spent is approximately a normal distribution. What are the times within which approximately 99.73 percent of all workers will fall? Multiple Choice [305.8, 520.2] [359.4, 466.6] [332.6, 493.4] [386.2, 439.8] [372.8, 453.2] (Chapter 3)

[332.6, 493.4] Explanation 3(26.8) − 413 = 332.6 3(26.8) + 413 = 493.4

Below we list several variables. Which of these variables are quantitative and which are qualitative? a. The dollar amount on an accounts receivable invoice. __________ b. The net profit for a company in 2017.__________. c. The stock exchange on which a company's stock is traded. __________ d. The national debt of the United States in 2017.__________ e. The advertising medium (radio, television, or print) used to promote a product.__________ (Chapter 1)

a. The dollar amount on an accounts receivable invoice. Quantitative b. The net profit for a company in 2017.Quantitative. c. The stock exchange on which a company's stock is traded. Qualitative d. The national debt of the United States in 2017.Quantitative e. The advertising medium (radio, television, or print) used to promote a product. Qualitative Explanation Quantitative; dollar amounts correspond to values on the real number line. Quantitative; net profit is a dollar amount. Qualitative; which stock exchange is a category. Quantitative; national debt is a dollar amount. Qualitative; which type of medium is a category.

As the coefficient of variation ________, risk ________. Multiple Choice decreases, increases increases, increases remains constant, increases increases, decreases (Chapter 3)

increases, increases Explanation The coefficient of variation can be used as a measure of risk because it can measure the rate on return.

The two types of quantitative variables are (Chapter 1)

interval and ratio. Explanation Nominative and ordinal are types of qualitative variables.

The number of miles a truck is driven before it is overhauled is an example of a(n) ________ variable. (Chapter 1)

ratio Explanation Nominative and ordinal are qualitative variables; miles driven can have a meaningful ratio.

A CFO is looking at what percentage of a company's resources are spent on computing. He samples companies in the pharmaceutical industry and develops the following stem-and-leaf display (leaf unit = 0.1). 5 269 6 255568999 7 11224557789 8 001222458 9 02455679 10 1556 11 137 12 13 255 What is the approximate shape of the distribution of the data? Multiple Choice skewed to the left uniform skewed to the right bimodal normal (Chapter 2)

skewed to the right Explanation With outliers at the stem of 13 and the majority of the data grouped around stems 6, 7, and 8, the shape is skewed with the outliers to the right.

If the mean, median, and mode for a given population are all equal and the relative frequency curve has matching tails to the right and left, then we would describe the shape of the distribution of the population as ________. Multiple Choice skewed to the right bimodal symmetrical Correct skewed to the left (Chapter 3)

symmetrical Explanation A symmetrical bell curve.

Pareto charts are frequently used to identify ________. outliers that do not show up on a dot plot the most common types of defects Correct random data the cause for extreme skewness to the right (Chapter 2)

the most common types of defects Explanation By definition, a defect is a flaw in a population or sample element.

(1) If we collect data on the number of wins the Dallas Cowboys earned each of the past 10 years, we have ________ data. (Chapter 1)

time series Explanation A time series is a collection of data taken over time, while a cross-section is a collection of data taken at the same point in time.

Sound City sells the TrueSound-XL, a top-of-the-line satellite car radio. Over the last 120 weeks, Sound City has sold no radios in five of the weeks, one radio in 28 of the weeks, two radios in 44 of the weeks, three radios in 26 of the weeks, four radios in 11 of the weeks, and five radios in 6 of the weeks. The following table summarizes this information. Number ofRadios Sold 0 1 2 3 4 5 Number of Weeks Having the Sales Amount 5 28 44 26 11 6 Compute a weighted mean that measures the average number of radios sold per week over the 120 weeks. (Chapter 3)

μ=2.23 Explanation Weighted Mean= ΣW1X1ΣW1μ =5 (0) + 28(1) + 44(2) + 26(3) + 11(4) + 6(5)120 = 2.23

Researchers wish to study fuel consumption rates based on speed. The data from the test car at 10 speeds are below. Speed Miles/Gallon 15 14 23 17 30 20 35 24 42 26 45 23 50 18 54 15 60 11 65 10 It can be shown that for these data: X¯¯¯ = 41.9, y¯ = 17.8, ∑10i=1 (xi − x¯)2 = 2352.9, ∑10i=1 (yi − y¯)2 = 267.6, ∑10i=1 (xi − x¯) (yi − y¯) = −270.2.X¯ = 41.9, y¯ = 17.8, ∑i=110 (xi - x¯)2 = 2352.9, ∑i=110 (yi - y¯)2 = 267.6, ∑i=110 (xi - x¯) (yi - y¯) = -270.2. Calculate the sample covariance. −30.02 −82.86 −27.02 −74.58 −270.2 (Chapter 3)

−30.02 Explanation Sxy=∑10i=1(xi − x¯)(yi − y¯)/(n−1)=−270.2/9=−30.02