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Q:
A the correlation is close to 0, then we expect to see
a. An upward sloping cluster of points on the scatterplot
b. A downward sloping cluster of points
c. A cluster of points around a trendline
d. A cluster of points with no apparent relationship
e. We cannot say what the scatterplot should look like based on the correlation
Q:
The limitation of covariance as a descriptive measure of association is that it
a. Only captures positive relationships
b. Does not capture the units of the variables
c. Is very sensitive to the units of the variables
d. Is invalid if one of the variables is categorical
e. None of these options
Q:
We can infer that there is a strong relationship between two numerical variables when
a. The points on a scatterplot cluster tightly around an upward sloping straight line
b. The points on a scatterplot cluster tightly around a downward sloping straight line
c. Either of these options
d. Neither of these options
Q:
Correlation and covariance measure
a. The strength of a linear relationship between two numerical variables
b. The direction of a linear relationship between two numerical variables
c. The strength and direction of a linear relationship between two numerical variables
d. The strength and direction of a linear relationship between two categorical variables
e. None of these options
Q:
Scatterplots are also referred to as
a. Crosstabs
b. Contingency charts
c. X-Y charts
d. All of these options
e. None of these options
Q:
We study relationships among numerical variables using
a. Correlation
b. Covariance
c. Scatterplots
d. All of these options
e. None of these options
Q:
A useful way of comparing the distribution of a numerical variable across categories of some categorical variable is
a. Side-by-side boxplots
b. Side-by-side histograms
c. Both of these options
d. Neither of these options
Q:
The most common data format is
a. Long
b. Short
c. Stacked
d. Unstacked
Q:
Example of comparison problems include
a. Salary broken down by male and female subpopulations
b. Cost of living broken down by region of a country
c. Recovery rate for a disease broken down by patients who have taken a drug and patients who have taken a placebo
d. Starting salary of recent graduates broken down by academic major
e. All of these options
Q:
The Excel function that allows you to count using more than one criterion is
a. COUNTIF
b. COUNTIFS
c. SUMPRODUCT
d. VLOOKUP
e. HLOOKUP
Q:
Tables used to display counts of a categorical variable are called
a. Crosstabs
b. Contingency tables
c. Both of these options
d. Neither of these options
Q:
To examine relationships between two categorical variables, we can use
a. Counts and corresponding charts of the counts
b. Scatterplots
c. Histograms
d. None of these options
Q:
A question of great interest to economists is how the distribution of family income has changed in the United States during the last 20 years. The summary measures and histograms shown below are generated for a sample of 500 family incomes, using the 1985 and 2005 income for each family in the sample.Summary Measures:Based on these results, discuss as completely as possible how the distribution of family income in the United States changed from 1985 to 2005.
Q:
Half of the job applicants scored below what value?
Q:
Seventy percent of the job applicants scored above what value?
Q:
How many job applicants scored above 50?
Q:
NARRBEGIN: SA_98_103
The histogram below represents scores achieved by 250 job applicants on a personality profile. NARREND How many job applicants scored between 10 and 30?
Q:
NARRBEGIN: SA_98_103
The histogram below represents scores achieved by 250 job applicants on a personality profile. NARREND What percentage of the job applicants scored below 60?
Q:
NARRBEGIN: SA_98_103
The histogram below represents scores achieved by 250 job applicants on a personality profile. NARREND What percentage of the job applicants scored between 30 and 40?
Q:
Based on the histogram shown below, how would you describe the salary distribution for these data?
Q:
Based on the histogram shown below, how would you describe the age distribution for these data?
Q:
NARRBEGIN: SA_95_97
A financial analyst collected useful information for 30 employees at Gamma Technologies, Inc. These data include each selected employees gender, age, number of years of relevant work experience prior to employment at Gamma, number of years of employment at Gamma, the number of years of post-secondary education, and annual salary.
NARREND
Indicate the type of data for each of the six variables included in this set.
Q:
The proportion of Americans under the age of 18 who are living below the poverty line for each of the years 1959 through 2000 is used to generate the following time series plot.How successful have Americans been recently in their efforts to win "the war against poverty" for the nation's children?
Q:
An operations management professor is interested in how her students performed on her midterm exam. The histogram shown below represents the distribution of exam scores (where the maximum score is 100) for 50 students. Based on this histogram, how would you characterize the students' performance on this exam?
Q:
The data below represents monthly sales for two years of beanbag animals at a local retail store (Month 1 represents January and Month 12 represents December). Given the time series plot below, do you see any obvious patterns in the data? Explain.
Q:
NARRBEGIN: SA_89_91
The following data represent the number of children in a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
NARREND
Is the distribution of the number of children symmetrical or skewed? Why?
Q:
NARRBEGIN: SA_89_91
The following data represent the number of children in a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
NARREND
Compute the median number of children.
Q:
NARRBEGIN: SA_89_91
The following data represent the number of children in a sample of 10 families from Chicago: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
NARREND
Compute the mean number of children.
Q:
NARRBEGIN: SA_86_88Suppose that an analysis of a set of test scores reveals that: , NARRENDCalculate the interquartile range. What does this tell you about the data?
Q:
NARRBEGIN: SA_86_88Suppose that an analysis of a set of test scores reveals that: , NARRENDWhat can you say about the relative position of each of the observations 34, 84, and 104?
Q:
NARRBEGIN: SA_86_88Suppose that an analysis of a set of test scores reveals that: , NARRENDWhat do these statistics tell you about the shape of the distribution?
Q:
How would you describe the salary of Virginia's teachers compared to those across the entire United States? Justify your answer.
Q:
NARRBEGIN: SA_82_85Below you will find summary measures on salaries for classroom teachers across the United States. You will also find a list of selected states and their average teacher salary. All values are in thousands of dollars.Salaries for classroom teachers across the United States SalaryCount51.000Mean35.890Median35.000Standard deviation 6.226Minimum26.300Maximum50.300Variance38.763First quartile31.550Third quartile40.050Selected states and their average teacher salaryStateSalaryAlabama31.3Colorado35.4Connecticut50.3Delaware40.5Nebraska31.5Nevada36.2New Hampshire35.8New Jersey47.9New Mexico29.6South Carolina31.6South Dakota26.3Tennessee33.1Texas32.0Utah30.6Vermont36.3Virginia35.0Wyoming31.6NARRENDWhat salary amount represents the second quartile?
Q:
NARRBEGIN: SA_82_85Below you will find summary measures on salaries for classroom teachers across the United States. You will also find a list of selected states and their average teacher salary. All values are in thousands of dollars.Salaries for classroom teachers across the United States SalaryCount51.000Mean35.890Median35.000Standard deviation 6.226Minimum26.300Maximum50.300Variance38.763First quartile31.550Third quartile40.050Selected states and their average teacher salaryStateSalaryAlabama31.3Colorado35.4Connecticut50.3Delaware40.5Nebraska31.5Nevada36.2New Hampshire35.8New Jersey47.9New Mexico29.6South Carolina31.6South Dakota26.3Tennessee33.1Texas32.0Utah30.6Vermont36.3Virginia35.0Wyoming31.6NARRENDWhich of the states listed paid their teachers average salaries that are below 75% of all average salaries?
Q:
NARRBEGIN: SA_82_85Below you will find summary measures on salaries for classroom teachers across the United States. You will also find a list of selected states and their average teacher salary. All values are in thousands of dollars.Salaries for classroom teachers across the United States SalaryCount51.000Mean35.890Median35.000Standard deviation 6.226Minimum26.300Maximum50.300Variance38.763First quartile31.550Third quartile40.050Selected states and their average teacher salaryStateSalaryAlabama31.3Colorado35.4Connecticut50.3Delaware40.5Nebraska31.5Nevada36.2New Hampshire35.8New Jersey47.9New Mexico29.6South Carolina31.6South Dakota26.3Tennessee33.1Texas32.0Utah30.6Vermont36.3Virginia35.0Wyoming31.6NARRENDWhich of the states listed paid their teachers average salaries that exceed at least 75% of all average salaries?
Q:
Explain what would cause the mean to be slightly lower than the median in this case.
Q:
NARRBEGIN: SA_79_81In an effort to provide more consistent customer service, the manager of a local fast-food restaurant would like to know the dispersion of customer service times about their average value for the facility's drive-up window. The table below provides summary measures for the customer service times (in minutes) for a sample of 50 customers collected over the past week.Count50.000Mean0.873Median0.885Standard deviation0.432Minimum0.077Maximum1.608Variance0.187Skewness-0.003NARRENDAre the empirical rule applicable in this case? If so, apply it and interpret your results. If not, explain why the empirical rule is not applicable here.
Q:
NARRBEGIN: SA_79_81In an effort to provide more consistent customer service, the manager of a local fast-food restaurant would like to know the dispersion of customer service times about their average value for the facility's drive-up window. The table below provides summary measures for the customer service times (in minutes) for a sample of 50 customers collected over the past week.Count50.000Mean0.873Median0.885Standard deviation0.432Minimum0.077Maximum1.608Variance0.187Skewness-0.003NARRENDInterpret the variance and standard deviation of this sample.
Q:
Generate a boxplot to summarize the data. What does the boxplot indicate?
Q:
NARRBEGIN: SA_76_78The data shown below contains family incomes (in thousands of dollars) for a set of 50 families; sampled in 1980 and 1990. Assume that these families are good representatives of the entire United States.198019901980199019801990 58 54 33 29 73 69 6 2 14 10 26 22 59 55 48 44 64 70 71 57 20 16 59 55 30 26 24 20 11 7 38 34 82 78 70 66 36 32 95 97 31 27 33 29 12 8 92 88 72 68 93 89115111100 96100102 62 58 1 0 51 47 23 19 27 23 22 18 34 30 22 47 50 75 36 61141166124149125150 72 97113138121146165190118143 88113 79104 96121 NARRENDThe Republicans claim that the country was better off in 1990 than in 1980, because the average income increased. Do you agree?
Q:
NARRBEGIN: SA_76_78The data shown below contains family incomes (in thousands of dollars) for a set of 50 families; sampled in 1980 and 1990. Assume that these families are good representatives of the entire United States.198019901980199019801990 58 54 33 29 73 69 6 2 14 10 26 22 59 55 48 44 64 70 71 57 20 16 59 55 30 26 24 20 11 7 38 34 82 78 70 66 36 32 95 97 31 27 33 29 12 8 92 88 72 68 93 89115111100 96100102 62 58 1 0 51 47 23 19 27 23 22 18 34 30 22 47 50 75 36 61141166124149125150 72 97113138121146165190118143 88113 79104 96121 NARRENDFind the mean, median, standard deviation, first and third quartiles, and the 95th percentile for family incomes in both years.
Q:
NARRBEGIN: SA_74_75
Statistics professor has just given a final examination in his statistical inference course. He is particularly interested in learning how his class of 40 students performed on this exam. The scores are shown below.
77 81 74 77 79 73 80 85 86 73
83 84 81 73 75 91 76 77 95 76
90 85 92 84 81 64 75 90 78 78
82 78 86 86 82 70 76 78 72 93
NARREND
Explain why the mean and median are different.
Q:
NARRBEGIN: SA_74_75
Statistics professor has just given a final examination in his statistical inference course. He is particularly interested in learning how his class of 40 students performed on this exam. The scores are shown below.
77 81 74 77 79 73 80 85 86 73
83 84 81 73 75 91 76 77 95 76
90 85 92 84 81 64 75 90 78 78
82 78 86 86 82 70 76 78 72 93
NARREND
What are the mean and median scores on this exam?
Q:
NARRBEGIN: SA_71_73
A manager for Marko Manufacturing, Inc. has recently been hearing some complaints that women are being paid less than men for the same type of work in one of their manufacturing plants. The boxplots shown below represent the annual salaries for all salaried workers in that facility (40 men and 34 women). NARREND
What can you say about the shape of the distributions given the boxplots above?
Q:
NARRBEGIN: SA_71_73
A manager for Marko Manufacturing, Inc. has recently been hearing some complaints that women are being paid less than men for the same type of work in one of their manufacturing plants. The boxplots shown below represent the annual salaries for all salaried workers in that facility (40 men and 34 women). NARREND
How large must a person's salary should be to qualify as an outlier on the high side? How many outliers are there in these data?
Q:
NARRBEGIN: SA_71_73
A manager for Marko Manufacturing, Inc. has recently been hearing some complaints that women are being paid less than men for the same type of work in one of their manufacturing plants. The boxplots shown below represent the annual salaries for all salaried workers in that facility (40 men and 34 women). NARREND
Would you conclude that there is a difference between the salaries of women and men in this plant? Justify your answer.
Q:
The median of a data set with 30 values would be the average of the 15th and the 16th values when the data values are arranged in ascending order.
Q:
Suppose that a sample of 8 observations has a standard deviation of 2.50, then the sum of the squared deviations from the sample mean is 17.50.
Q:
There are four quartiles that divide the values in a data set into four equal parts.
Q:
The difference between the largest and smallest values in a data set is called the range.
Q:
The value of the mean times the number of observations equals the sum of all of the data values.
Q:
Expressed in percentiles, the interquartile range is the difference between the 25th and 75th percentiles.
Q:
Abby has been keeping track of what she spends to rent movies. The last seven week's expenditures, in dollars, were 6, 4, 8, 9, 6, 12, and 4. The mean amount Abby spends on renting movies is $7.
Q:
Assume that the histogram of a data set is symmetric and bell shaped, with a mean of 75 and standard deviation of 10. Then, approximately 95% of the data values were between 55 and 95.
Q:
The median is one of the most frequently used measures of variability.
Q:
The standard deviation is measured in original units, such as dollars and pounds.
Q:
The difference between the first and third quartiles is called the interquartile range.
Q:
The value of the standard deviation always exceeds that of the variance.
Q:
In a positively skewed distribution, the mean is smaller than the median and the median is smaller than the mode.
Q:
The length of the box in the boxplot portrays the interquartile range.
Q:
The mean is a measure of central location.
Q:
If a histogram has a single peak and looks approximately the same to the left and right of the peak, we should expect no difference in the values of the mean, median, and mode.
Q:
Suppose that a sample of 10 observations has a standard deviation of 3, then the sum of the squared deviations from the sample mean is 30.
Q:
A histogram is said to be symmetric if it has a single peak and looks approximately the same to the left and right of the peak.
Q:
Both ordinal and nominal variables are categorical.
Q:
Distribution is a general term used to describe the way data are distributed, as indicated by a frequency table or histogram.
Q:
Cross-sectional data are data on a population at a distinct point in time, whereas time series data are data collected across time.
Q:
Phone numbers, Social Security numbers, and zip codes are examples of numerical variables.
Q:
A variable (or field) is an attribute, or measurement, on members of a population, whereas an observation (or case or record) is a list of all variable values for a single member of a population.
Q:
The number of car insurance policy holders is an example of a discrete random variable.
Q:
Time series data are often graphically depicted on a line chart, which is a plot of the variable of interest over time.
Q:
In the term "frequency table," frequency refers to the number of data values falling within each category.
Q:
A frequency table indicates how many observations fall within each category, and a histogram is its graphical analog.
Q:
A population includes all elements or objects of interest in a study, whereas a sample is a subset of the population used to gain insights into the characteristics of the population.
Q:
Some histograms have two or more peaks. This is often an indication that the data come from two or more distinct populations.
Q:
A skewed histogram is one with a long tail extending either to the right or left. The former is called negatively skewed, and the later is called positively skewed.
Q:
Categorical variables can be classified as either discrete or continuous.
Q:
Four different shapes of histograms are commonly observed: symmetric, positively skewed, negatively skewed, and bimodal.
Q:
All nominal data may be treated as ordinal data.
Q:
Data can be categorized as cross-sectional or time series.