Question 1

The following data represent the weights (in kilograms) of a sample of 30 horses: Weight
$$\begin{array} { l } 
165 \
175 \
150 \
155 \
173 \
149 \
145 \
153 \
153 \
153 \
152 \
145 \
164 \
143 \
170 \
175 \
148 \
174 \
171 \
156 \
166 \
168 \
152 \
150 \
173 \
168 \
146 \
155 \
172 \
159
\end{array}$$ Compute the range and interquartile range of the data.

Accepted Answer

The answer of The following data represent the weights (in...

Question 2

The following data represent the ages (in years) of a sample of 25 employees from a government
department: $$\begin{array} { | l | l | l | l | r | r | r | r | r | r | } 
\hline 31 & 43 & 56 & 23 & 49 & 42 & 33 & 61 & 44 & 28 \
\hline 48 & 38 & 44 & 35 & 40 & 64 & 52 & 42 & 47 & 39 \
\hline 53 & 27 & 36 & 35 & 20 & & & & & \
\hline
\end{array}$$ Find the range of ages.

Accepted Answer

The answer of The following data represent the ages (in...

Question 3

A courier company is reviewing their delivery times. The following descriptive statistics relates to this courier company. The mean time for package delivery is 5 hours, the first quartile is 4 hours, the third quartile is 17 hours. This means that 50% of deliveries take more than 5 hours?

Accepted Answer

A) True 
 B)False

Question 4

A sample of eight observations of variables x and y is shown below: $$\begin{array} { | l | r | r | r | r | r | r | r | r | } 
\hline x & 5 & 3 & 7 & 9 & 2 & 4 & 6 & 8 \
\hline y & 20 & 23 & 15 & 11 & 27 & 21 & 17 & 14 \
\hline
\end{array}$$ Calculate the covariance and the coefficient of correlation, and comment on the relationship between X and Y.

Accepted Answer

The answer of A sample of eight observations of variables...

Question 5

The range is considered the weakest measure of variability.

Accepted Answer

A) True 
 B)False

Question 6

A supermarket has determined that daily demand for egg cartons has an approximate mound-shaped distribution, with a mean of 55 cartons and a standard deviation of 6 cartons.
a. For what percentage of days can we expect the number of cartons of eggs sold to be between 49 and 61?
b. For what percentage of days can we expect the number of cartons of eggs sold to be more than 2 standard deviations from the mean?
c. If the supermarket begins each morning with a stock of 77 cartons of eggs, for what percentage of days will there be an insufficient number of cartons to meet the demand?

Accepted Answer

The answer of A supermarket has determined that daily demand...

Question 7

How is the value of the correlation coefficient r affected in each of the following cases?
a. Each x value is multiplied by 4.
b. Each x value is switched with the corresponding y value.
c. Each x value is increased by 2.

Accepted Answer

The answer of How is the value of the correlation...

Question 8

When is the standard deviation of a data set smaller than its variance? Explain.

Accepted Answer

The answer of When is the standard deviation of a...

Question 9

The empirical rule states that the percentage of observations in a data set (provided that the data set has a bell-shaped and symmetric distribution) that fall within one standard deviation of their mean is
approximately 75%.

Accepted Answer

A) True 
 B)False

Question 10

Suppose that an analysis of a set of data reveals that $Q _ { 1 } = 45,$ $Q _ { 2 } = 85$ and $Q _ { 3 } = 105$ 
a. What do these statistics tell you about the shape of the distribution?
b. What can you say about the relative position of each of the observations 34, 84 and 104?
c. Calculate the interquartile range.
d. What does the interquartile range tell you about the data?

Accepted Answer

The answer of Suppose that an analysis of a set...

Question 11

Chebyshev's theorem states that the percentage of observations in a data set that should fall within 3 standard deviations of their mean is at least 88.9%.

Accepted Answer

A) True 
 B)False

Question 12

The coefficient of variation gives an indication of the magnitude of the standard deviation relative to the mean.

Accepted Answer

A) True 
 B)False

Question 13

The following data represent the ages (in years) of a sample of 25 employees from a government
department: $$\begin{array} { | l | l | l | l | r | r | r | r | r | r | } 
\hline 31 & 43 & 56 & 23 & 49 & 42 & 33 & 61 & 44 & 28 \
\hline 48 & 38 & 44 & 35 & 40 & 64 & 52 & 42 & 47 & 39 \
\hline 53 & 27 & 36 & 35 & 20 & & & & & \
\hline
\end{array}$$ Compute the 8th decile of the data.

Accepted Answer

The answer of The following data represent the ages (in...

Question 14

Generally speaking, if two variables have a strong positive linear relationship, the covariance between them is equal to one.

Accepted Answer

A) True 
 B)False

Question 15

The shape of the distribution helps to determine the best measure of central location and variability in a data set.

Accepted Answer

A) True 
 B)False

Question 16

A linear regression model estimating the relationship between Expenditure on imports ($) and Annual household income ($) is as follows:
Estimated Expenditure on Imports = 1.35 + 0.11Annual household income.
Interpret the slope.

Accepted Answer

The answer of A linear regression model estimating the relationship...

Question 17

A linear regression model estimating the relationship between Expenditure on Imports and Annual household income has an R2 value of 0.81.
Interpret R2.

Accepted Answer

The answer of A linear regression model estimating the relationship...

Question 18

In a symmetric distribution, the mean is the most used measure of central location for quantitative data.

Accepted Answer

A) True 
 B)False

Question 19

A data sample has a mean of 107, a median of 122 and a mode of 134. The distribution of the data is positively skewed.

Accepted Answer

A) True 
 B)False

Question 20

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline 26.5 & 23.5 & 29.7 & 24.8 & 21.1 & 24.3 & 20.4 \
\hline 22.7 & 27.2 & 23.7 & 24.1 & 24.8 & 28.2 & \
\hline
\end{array}$$ Compute the coefficient of variation.

Accepted Answer

The answer of The following data represent the salaries (in...

Exam 5: Numerical Descriptive Measures

A courier company is reviewing their delivery times. The following descriptive statistics relates to this courier company. The mean time for package delivery is 5 hours, the first quartile is 4 hours, the third quartile is 17 hours. This means that 50% of deliveries take more than 5 hours?

The range is considered the weakest measure of variability.

How is the value of the correlation coefficient r affected in each of the following cases? a. Each x value is multiplied by 4. b. Each x value is switched with the corresponding y value. c. Each x value is increased by 2.

When is the standard deviation of a data set smaller than its variance? Explain.

The empirical rule states that the percentage of observations in a data set (provided that the data set has a bell-shaped and symmetric distribution) that fall within one standard deviation of their mean is approximately 75%.

Chebyshev's theorem states that the percentage of observations in a data set that should fall within 3 standard deviations of their mean is at least 88.9%.

The coefficient of variation gives an indication of the magnitude of the standard deviation relative to the mean.

Generally speaking, if two variables have a strong positive linear relationship, the covariance between them is equal to one.

The shape of the distribution helps to determine the best measure of central location and variability in a data set.

A linear regression model estimating the relationship between Expenditure on imports ($) and Annual household income ($) is as follows: Estimated Expenditure on Imports = 1.35 + 0.11Annual household income. Interpret the slope.

A linear regression model estimating the relationship between Expenditure on Imports and Annual household income has an R2 value of 0.81. Interpret R2.

In a symmetric distribution, the mean is the most used measure of central location for quantitative data.

A data sample has a mean of 107, a median of 122 and a mode of 134. The distribution of the data is positively skewed.