Question 1

A linear regression model estimating the relationship between Expendure on Imports and Annual household income has an r value of 0.90.
Interpret r.

Accepted Answer

A r of 0.90 means that there i

Question 2

Given the following sample data: $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | c | } 
\hline x & 420 & 610 & 625 & 500 & 400 & 450 & 550 & 650 & 480 & 565 \
\hline y & 2.80 & 3.60 & 3.75 & 3.00 & 2.50 & 2.70 & 3.50 & 3.90 & 2.95 & 3.30 \
\hline
\end{array}$$ a. calculate the covariance and the correlation coefficient.
b. comment on the relationship between X and Y.
c. determine the least-squares line.
d. draw the scatter diagram and plot the least-squares line.

Accepted Answer

a. @#LAT-DLM& @#LAT-DLM& b. There is a very strong

Question 3

Which of the following are measures of the linear relationship between two variables?

Accepted Answer

A)  The covariance. 
B)  The coefficient of correl ation. 
C)  The coefficient of determination. 
D)  All of these choices are correct. 
A)  The covariance. 
B)  The coefficient of correl ation. 
C)  The coefficient of determination. 
D)  All of these choices are correct.

Question 4

A student scores 87, 73, 92 and 86 on four exams during the semester, and 95 on the final exam. If the final is weighted double and the four others weighted equally, the student's final average would be 88.

Accepted Answer

A) True 
 B)False

Question 5

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

@#LAT-DLM& @#LAT-DLM& There is a very st

Question 6

The average score for a class of 30 students was 75. The 20 male students in the class averaged 70. The female students in the class averaged:

Accepted Answer

A)  75 . 
B)  85 . 
C)  65 . 
D)  70 . 
E)  80 . 
A)  75 . 
B)  85 . 
C)  65 . 
D)  70 . 
E)  80 .

Question 7

The following data represent the numbers of bedrooms in a sample of 10 suburban houses in Melbourne: $$\begin{array} { | l | l | l | l | r | r | r | r | r | r | } 
\hline 3 & 3 & 2 & 2 & 4 & 5 & 2 & 5 & 4 & 2 \
\hline
\end{array}$$ Use these data to answer the following question/s.
-a. Compute the mean.
b. Compute the median.

Accepted Answer

a. mean =

Question 8

Lily has been keeping track of what she spends on eating out. The last week's expenditures for meals eaten out were $5.69, $5.95, $6.19, $10.91, $7.49, $14.53 and $7.66. The mean amount Lily spends on meals is $8.35.

Accepted Answer

A) True 
 B)False

Question 9

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 lower quartile.

Accepted Answer

= 3.5.
(22.7 + 0.50(

Question 10

The following data represent the weights (in kilograms) of a sample of 30 horses:
Weight
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
Are there any outliers?

Accepted Answer

Q₃ = 170.25, Q₁ = 150.

Question 11

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 12

A linear regression model estimating the relationship between Expenditure on exports ($) and Annual household income ($) is as follows:
Estimated Expenditure on Exports = 3.55 − 0.02Annual household income
Interpret the slope.

Accepted Answer

We estimate, that for each ext

Question 13

The following data represent the weights (in kilograms) of a sample of 30 horses:
Weight
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
Compute the sample variance and sample standard deviation.

Accepted Answer

s² = 113.10

Question 14

Using percentiles, the difference between which of the following is the interquartile range?

Accepted Answer

A)  $10 \%$ and $90 \%$ values. 
B)  $25 \%$ and $75 \%$ values. 
C)  $15 \%$ and $85 \%$ values. 
D)  $30 \%$ and $70 \%$ values. 
A)  $10 \%$ and $90 \%$ values. 
B)  $25 \%$ and $75 \%$ values. 
C)  $15 \%$ and $85 \%$ values. 
D)  $30 \%$ and $70 \%$ values.

Question 15

The following data represent the ages (in years) of a sample of 25 employees from a government
department: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline 31 & 43 & 56 & 23 & 49 & 42 & 33 & 61 & 44 & 28 \
\hline 48 & 38 & 44 & 35 & 40 & 64 & 52 & 42 & 47 & 39 \
\hline 53 & 27 & 36 & 35 & 20 & & & & & \
\hline
\end{array}$$ Calculate the 1st quintile. (Hint: 1st quintile is L20)

Accepted Answer

Location of 1st quin

Question 16

According to Chebyshev's theorem, which of the following is the percentage of measurements in a data set that fall within three standard deviations of their mean?

Accepted Answer

A)  $75 \%$. 
B)  At least 75\%. 
C)  $89 \%$. 
D)  At least $89 \%$. 
A)  $75 \%$. 
B)  At least 75\%. 
C)  $89 \%$. 
D)  At least $89 \%$.

Question 17

According to the empirical rule, which of the following is the approximate percentage of measurements in a data set (provided that the data set has a bell-shaped distribution) that fall within two standard deviations of their mean?

Accepted Answer

A)  $68 \%$. 
B)  $75 \%$. 
C)  $95 \%$ 
D)  $99 \%$. 
A)  $68 \%$. 
B)  $75 \%$. 
C)  $95 \%$ 
D)  $99 \%$.

Question 18

Which of the following statements is true?

Accepted Answer

A) The standard deviation is always greater than the variance. 
B) The sum of the squared deviations from the mean is always zero. 
C) The standard deviation is in squared units. 
D) The sum of the deviations from each value in a data set to the mean, is always zero. 
A) The standard deviation is always greater than the variance. 
B) The sum of the squared deviations from the mean is always zero. 
C) The standard deviation is in squared units. 
D) The sum of the deviations from each value in a data set to the mean, is always zero.

Question 19

a. Calculate the covariance and the coefficient of correlation for the following sample. $$\begin{array} { | l | r | r | r | r | r | } 
\hline x & 9 & 6 & 7 & 5 & 8 \
\hline y & 19 & 14 & 16 & 12 & 15 \
\hline
\end{array}$$ b. What do these statistics tell you about the relationship between X and Y?

Accepted Answer

a. @#LAT-DLM& @#LAT-DLM& b. The covariance tells u

Question 20

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

a. Approximately 68%

Exam 5: Numerical Descriptive Measures

A linear regression model estimating the relationship between Expendure on Imports and Annual household income has an r value of 0.90. Interpret r.

Which of the following are measures of the linear relationship between two variables?

A student scores 87, 73, 92 and 86 on four exams during the semester, and 95 on the final exam. If the final is weighted double and the four others weighted equally, the student's final average would be 88.

A sample of eight observations of variables x and y is shown below: x 5 3 7 9 2 4 6 8 y 20 23 15 11 27 21 17 14 Calculate the covariance and the coefficient of correlation, and comment on the relationship between X and Y.

The average score for a class of 30 students was 75. The 20 male students in the class averaged 70. The female students in the class averaged:

The following data represent the numbers of bedrooms in a sample of 10 suburban houses in Melbourne: 3 3 2 2 4 5 2 5 4 2 Use these data to answer the following question/s. -a. Compute the mean. b. Compute the median.

Lily has been keeping track of what she spends on eating out. The last week's expenditures for meals eaten out were $5.69, $5.95, $6.19, $10.91, $7.49, $14.53 and $7.66. The mean amount Lily spends on meals is $8.35.

The following data represent the salaries (in thousands of dollars) of a sample of 13 employees of a firm: 26.5 23.5 29.7 24.8 21.1 24.3 20.4 22.7 27.2 23.7 24.1 24.8 28.2 Compute the lower quartile.

The following data represent the weights (in kilograms) of a sample of 30 horses: Weight 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 Are there any outliers?

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

A linear regression model estimating the relationship between Expenditure on exports ($) and Annual household income ($) is as follows: Estimated Expenditure on Exports = 3.55 − 0.02Annual household income Interpret the slope.

The following data represent the weights (in kilograms) of a sample of 30 horses: Weight 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 Compute the sample variance and sample standard deviation.

Using percentiles, the difference between which of the following is the interquartile range?

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Calculate the 1st quintile. (Hint: 1st quintile is L20)

According to Chebyshev's theorem, which of the following is the percentage of measurements in a data set that fall within three standard deviations of their mean?

According to the empirical rule, which of the following is the approximate percentage of measurements in a data set (provided that the data set has a bell-shaped distribution) that fall within two standard deviations of their mean?

Which of the following statements is true?

a. Calculate the covariance and the coefficient of correlation for the following sample. x 9 6 7 5 8 y 19 14 16 12 15 b. What do these statistics tell you about the relationship between X and Y?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

The following data represent the ages (in years) of a sample of 25 employees from a government department: 31 43 56 23 49 42 33 61 44 28 48 38 44 35 40 64 52 42 47 39 53 27 36 35 20 Calculate the 1st quintile. (Hint: 1^st quintile is L₂₀)