Assignment 1 | Complete Solution

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Question 1 (2 points)
 
Both ordinal and nominal variables are categorical.
Question 1 options:
 
True
 
False
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Question 2 (2 points)
 
The time required to drive from Detroit to Lansing is an example of a discrete random variable.
Question 2 options:
 
True
 
False
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Question 3 (2 points)
 
Phone numbers, Social Security numbers, and zip codes are examples of numerical variables.
Question 3 options:
 
True
 
False
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Question 4 (2 points)
 
If you are in a class where most students do reasonably well on a test but a few pull down the class average, the histogram describing the test scores will indicate a positively-skewed distribution.
Question 4 options:
 
True
 
False
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Question 5 (2 points)
 
Some histograms have two or more peaks. This is often an indication that the data come from two or more distinct populations.
Question 5 options:
 
True
 
False
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Question 6 (2 points)
 
Statisticians often refer to the pivot tables as contingency tables or crosstabs.
Question 6 options:
 
True
 
False
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Question 7 (2 points)
 
The scatterplot is a graphical technique used to describe the relationship between two numerical variables.
Question 7 options:
 
True
 
False
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Question 8 (2 points)
 
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.
Question 8 options:
 
True
 
False
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Question 9 (2 points)
 
A data sample has a mode of 140, a median of 130, and a mean of 120. The distribution of the data is positively skewed.
Question 9 options:
 
True
 
False
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Question 10 (4 points)
 
Suppose that a sample of 8 observations has a sample variance of 2.50, then the sum of the squared deviations from the sample mean is 17.50.
Question 10 options:
 
True
 
False
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Question 11 (2 points)
 
If two data sets have the same range, the smallest and largest observations in both sets should be the same
Question 11 options:
 
True
 
False
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Question 12 (2 points)
 
The standard deviation is measured in original units, such as dollars and pounds.
Question 12 options:
 
True
 
False
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Question 13 (2 points)
 
The median is one of the most frequently used measures of variability.
Question 13 options:
 
True
 
False
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Question 14 (2 points)
 
It is possible that the data points are close to a curve and have a correlation close to 0, because correlation is relevant only for measuring linear relationships.
Question 14 options:
 
True
 
False
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Question 15 (2 points)
 
Numerical variables can be subdivided into which two types?
Question 15 options:
 
Diverse and categorical
 
Discrete and continuous
 
Nominal and progressive
 
Cross-sectional and discrete
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Question 16 (2 points)
 
A sample of a population taken at one particular point in time is categorized as:
Question 16 options:
 
categorical
 
discrete
 
cross-sectional
 
time-series

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Question 17 (2 points)
 
A scatterplot allows one to see:
Question 17 options:
 
whether there is any relationship between two variables
 
what type of relationship there is between two variables
 
Both (a) and (b) are correct
 
Neither (a) nor (b) is correct
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Question 18 (2 points)
 
A bimodal histogram is often an indication that the:
Question 18 options:
 
data are incorrect
 
data are inconclusive
 
sample is not representative of the population
 
data come from two or more distinct populations
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Question 19 (2 points)
 
A population includes:
Question 19 options:
 
only people
 
only households
 
all objects of interest in a particular study
 
only machines
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Question 20 (4 points)
 
Which of the following statements are false?
Question 20 options:
 
A categorical variable is nominal if there is natural ordering of its possible values.
 
A variable is numerical if meaningful arithmetic can be performed on it.
 
Zip codes are usually treated as categorical variables, although they appear to be numerical.
 
All of the above
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Question 21 (4 points)
 
Which of the following are true statements of pivot tables?
Question 21 options:
 
They allow us to "slice and dice" data in a variety of ways.
 
Statisticians often refer to them as contingency tables or crosstabs.
 
Pivot tables can list counts, averages, sums, and other summary measures, whereas contingency tables list only counts.
 
All of the options.

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Question 22 (2 points)
 
Which of the following are considered measures of association?
Question 22 options:
 
Mean and variance
 
Variance and correlation
 
Correlation and covariance
 
Covariance and variance
 
First quartile and third quartile
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Question 23 (2 points)
 
The mode is best described as the
Question 23 options:
 
middle observation
 
same as the average
 
50th percentile
 
most frequently occurring value
 
third quartile
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Question 24 (2 points)
 
Which of the following statistics is not a measure of central location?
Question 24 options:
 
Mean
 
Median
 
Mode
 
Interquartile range
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Question 25 (2 points)
 
The correlation coefficient is always a value between
Question 25 options:
 
- 1 and 0
 
0 and +1
 
0.0 and 100
 
-1 and +1
 
-1 and 100
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Question 26 (2 points)
 
For a boxplot, the vertical line inside the box indicates the location of the
Question 26 options:
 
mean
 
median
 
mode
 
minimum value
 
maximum value

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Question 27 (2 points)
 
For a boxplot, the box itself represents what percent of the observations?
Question 27 options:
 
lower 25%
 
middle 50%
 
upper 75%
 
upper 90%
 
100%
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Question 28 (2 points)
 
Which of the following statements is true?
Question 28 options:
 
The sum of the deviations from the mean is always zero
 
The sum of the squared deviations from the mean is always zero
 
The range is always smaller than the variance
 
The standard deviation is always smaller than the variance
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Question 29 (4 points)
 
A sample of 20 observations has a standard deviation of 4. The sum of the squared deviations from the sample mean is:
Question 29 options:
 
400
 
320
 
304
 
288
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Question 30 (4 points)
 
A data set from a sample of 399 Michigan families was collected. The characteristics of the data include family size (large or small), number of cars owned by family (1, 2, 3, or 4), and whether family owns a foreign car. Excel produced the pivot table shown below.

 
Use this pivot table to determine how family size and number of cars owned influence the likelihood that a family owns a foreign car.
Question 30 options:
 

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Question 31 (4 points)
 
A real estate agent has gathered information on 40 houses that were recently sold in a local community. The data she collected represent the following variables: the selling price of each house (in thousands of dollars), the appraised value of each house (in thousands of dollars), the size of the house (in hundreds of square feet), and the number of bedrooms.

 
Indicate whether each of the four variables is continuous or discrete.
Question 31 options:
 

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Question 32 (2 points)
 
A recent survey data collected from 1000 randomly selected Internet users. The characteristics of the users include their gender, age, education, marital status and annual income. Using Excel, the following pivot tables were produced.
 
 
 
 
Approximate the percentage of these Internet users who are married with formal education beyond high school.
 
Question 32 options:
 

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Question 33 (2 points)
 
A recent survey data collected from 1000 randomly selected Internet users. The characteristics of the users include their gender, age, education, marital status and annual income. Using Excel, the following pivot tables were produced.
 
 
 
 
Approximate the percentage of these Internet users who are in the 58-71 age group.
Question 33 options:
 

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Question 34 (2 points)
 
The histogram below represents scores achieved by 250 job applicants on a personality profile.
 

 
Sixty percent of the job applicants scored below what value?
Question 34 options:
 

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Question 35 (2 points)
 
The histogram below represents scores achieved by 250 job applicants on a personality profile.
 

 
How many job applicants scored between 10 and 30?
Question 35 options:
 

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Question 36 (4 points)
 
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).
 
Would you conclude that there is a difference between the salaries of women and men in this plant? Justify your answer.
Question 36 options:
 

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Question 37 (6 points)
 
A 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

 
What are the mean and median scores on this exam? Explain why the mean and median are different.
Question 37 options:
 

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Question 38 (2 points)
 
An economic development researcher wants to understand the relationship between the average monthly expenditure on utilities for households in a particular middle-class neighborhood and each of the following household variables: family size, approximate location of the household within the neighborhood, and indication of whether those surveyed owned or rented their home, gross annual income of the first household wage earner, gross annual income of the second household wage earner (if applicable), size of the monthly home mortgage or rent payment, and the total indebtedness (excluding the value of a home mortgage) of the household.

 
The correlation for each pairing of variables is shown in the table below:
 
Table of correlations
 
 
Which of the variables appears to have the weakest linear relationship with the household’s average monthly expenditure on utilities?

 
Question 38 options:
 

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Question 39 (6 points)
 
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.
•    Compute the mean number of children.
•    Compute the median number of children.
•    Is the distribution of the number of children symmetrical or skewed? Why?
Question 39 options:
 

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