Question 1

There is ____________________ error in estimating a mean than in predicting an individual value.

Accepted Answer

The answer of There is ____________________ error in estimating a...

Question 2

Allman Brothers Concert
At a recent Allman Brothers concert,a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year.The following data were collected:
 $$\begin{array}{l}
\begin{array} { | l | c c c c c c c c c c | } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number af Concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}\\
\begin{array} { | l | c c c c c c c c c c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & \text { 38 } & 52 \
\hline \text { Number af Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}
\end{array}$$ An Excel output follows: 
-{Allman Brothers Concert Narrative} Draw a scatter diagram of the data.Comment on whether it appears that a linear model might be appropriate to describe the relationship between the age and number of concerts attended by the respondents.

Accepted Answer

The answer of Allman Brothers Concert
At a recent Allman Brothers...

Question 3

A medical statistician wanted to examine the relationship between the amount of sunshine (x)and incidence of skin discolorations (y).As an experiment he found the number of skin discolorations detected per 100,000 of population and the average daily sunshine in eight counties around the country.These data are shown below.
 $$\begin{array} {| l | c c c c c c c c | } 
\hline \text { Average Daily Sumshine } & 5 & 7 & 6 & 7 & 8 & 6 & 4 & 3 \
\hline \text { Skin Discolorations per 100,000 } & 7 & 11 & 9 & 12 & 15 & 10 & 7 & 5 \
\hline
\end{array}$$ Predict with 95% confidence the skin discolorations per 100,000 in a county with a daily average of 6.5 hours of sunshine.

Accepted Answer

The answer of A medical statistician wanted to examine the...

Question 4

Sunshine and Melanoma
A medical researcher wanted to examine the relationship between the amount of sunshine (x)in hours,and incidence of melanoma,a type of skin cancer (y).As an experiment he found the number of melanoma cases detected per 100,000 of population and the average daily sunshine in eight counties around the country.These data are shown below.
 $\begin{array}{|l|cccccccc|}
\hline\text { Average Daily Sunshine } & 5 & 7 & 6 & 7 & 8 & 6 & 4 & 3 \
\hline \text { Melanoma per } 100,000 & 7 & 11 & 9 & 12 & 15 & 10 & 7 & 5\
\hline 
\end{array}$ 
-{Sunshine and Melanoma Narrative} Estimate the number of skin cancer cases per 100,000 people who live in a state that gets 6 hours of sunshine on average.

Accepted Answer

The answer of Sunshine and Melanoma
A medical researcher wanted to...

Question 5

Grateful Dead Concert
At a recent Grateful Dead concert,a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year.It is suspected that older concert goers tend to go to more of his concerts in one year than younger concert goers.The data and analysis are shown below.
 $$\begin{array}{l}
\begin{array} { | l | c c c c c c c c c c | } 
\hline \text { AEe } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number af Concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}\\
\begin{array} { | l | c c c c c c c c c c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}
\end{array}$$ An Excel output follows: 
-{Grateful Dead Concert Narrative} Conduct a test of the population slope to determine at the 5% significance level whether a positive linear relationship exists between age and number of concerts attended.

Accepted Answer

The answer of Grateful Dead Concert
At a recent Grateful Dead...

Question 6

Oil Quality and Price
Quality of oil is measured in API gravity degrees--the higher the degrees API,the higher the quality.The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel.
 $$\begin{array} { | c | c | } 
\hline \text { Oi degrees API } & \text { Price per barrel (in \$) } \
\hline 27.0 & 12.02 \
28.5 & 12.04 \
30.8 & 12.32 \
31.3 & 12.27 \
31.9 & 12.49 \
34.5 & 12.70 \
34.0 & 12.80 \
34.7 & 13.00 \
37.0 & 13.00 \
41.0 & 13.17 \
41.0 & 13.19 \
38.8 & 13.22 \
39.3 & 13.27 \
\hline
\end{array}$$ A partial Minitab output follows:
 $$\begin{array}{l}
\text { Dascriptive atafistics }\
\begin{array} { l l l l l } 
\text { Variable } & \mathrm { N } & \text { Mear } & \text { StDev } & \text { SE Mear } \
\text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \
\text { Price } & 13 & 1270 & 0.757 & 0.127
\end{array}
\end{array}$$ $$\begin{array}{l}

\begin{array} { l l } 
\text { Covariances }&&\
&\text { Degeres } & \text { Price } \
\text { Degeres } &21.281667 & \
\text { Price } &2.026750 & 0.208933
\end{array}
\end{array}$$  $$\begin{array}{l}
\text { Analysis of Variance }\
\begin{array} { l l r r r } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text {p}\
\text { Regeression } & 1 & 2.3162 & 2.3162 & 134.24&0.000 \
\text { Resichul Entar } & 11 & 0.1898 & 0.0173 & \
\text { Total } & 12 & 2.5060 & &
\end{array}
\end{array}$$
-If the coefficient of determination is 1.0,then the coefficient of correlation must be 1.0.

Accepted Answer

A) True 
 B)False

Question 7

A prediction interval is used when we want to predict a one-time occurrence for a particular value of y when the independent variable is a given x value.

Accepted Answer

A) True 
 B)False

Question 8

The vertical spread of the data points about the regression line is measured by the y-intercept.

Accepted Answer

A) True 
 B)False

Question 9

If cov(x,y)= 1260, $s _ { x } ^ { 2 } = 1600$ ,and $s _ { y } ^ { 2 } = 1225$ ,then the coefficient of determination is:

Accepted Answer

A)  0.90 
B)  1.23 
C)  0.81 
D)  0.006

Question 10

Wayne Newton Concert
At a recent Wayne Newton concert,a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year.The following data were collected:
 $$\begin{array}{l}
\begin{array} { | l | c c c c c c c c c c| } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number af Concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}\\
\begin{array} { | l | c c c c c c c c c c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number af Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}
\end{array}$$ An Excel output follows: 
-{Oil Quality and Price Narrative} Estimate with 95% confidence the average oil price per barrel for an API degree of 35.

Accepted Answer

The answer of Wayne Newton Concert
At a recent Wayne Newton...

Question 11

A zero population correlation coefficient for x and y means that there is no type of relationship whatsoever between x and y.

Accepted Answer

A) True 
 B)False

Question 12

Cost of Textbooks
The editor of a higher education book publisher claims that a large part of the cost of books is the cost of paper.This implies that larger textbooks will cost more money.As an experiment to analyze the claim,a university student visits the bookstore and records the number of pages and the selling price of twelve randomly selected textbooks.These data are listed below.
 $$\begin{array} { | c | c | c | } 
\hline \text { Textbouk } & \text { Number af Peges } & \text { Selling Price (\$) } \
\hline 1 & 844 & 55 \
2 & 727 & 50 \
3 & 360 & 35 \
4 & 915 & 60 \
5 & 295 & 30 \
6 & 706 & 50 \
7 & 410 & 40 \
8 & 905 & 53 \
9 & 1058 & 65 \
10 & 865 & 54 \
11 & 677 & 42 \
12 & 912 & 58 \
\hline
\end{array}$$
-{Cost of Textbooks Narrative} Interpret the value of the slope of the regression line.

Accepted Answer

The answer of Cost of Textbooks
The editor of a higher...

Question 13

Oil Quality and Price
Quality of oil is measured in API gravity degrees--the higher the degrees API,the higher the quality.The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel.
 $$\begin{array} { | c | c | } 
\hline \text { Oi degrees API } & \text { Price per barrel (in \$) } \
\hline 27.0 & 12.02 \
28.5 & 12.04 \
30.8 & 12.32 \
31.3 & 12.27 \
31.9 & 12.49 \
34.5 & 12.70 \
34.0 & 12.80 \
34.7 & 13.00 \
37.0 & 13.00 \
41.0 & 13.17 \
41.0 & 13.19 \
38.8 & 13.22 \
39.3 & 13.27 \
\hline
\end{array}$$ A partial Minitab output follows:
 $$\begin{array}{l}
\text { Dascriptive atafistics }\
\begin{array} { l l l l l } 
\text { Variable } & \mathrm { N } & \text { Mear } & \text { StDev } & \text { SE Mear } \
\text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \
\text { Price } & 13 & 1270 & 0.757 & 0.127
\end{array}
\end{array}$$ $$\begin{array}{l}

\begin{array} { l l } 
\text { Covariances }&&\
&\text { Degeres } & \text { Price } \
\text { Degeres } &21.281667 & \
\text { Price } &2.026750 & 0.208933
\end{array}
\end{array}$$  $$\begin{array}{l}
\text { Analysis of Variance }\
\begin{array} { l l r r r } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text {p}\
\text { Regeression } & 1 & 2.3162 & 2.3162 & 134.24&0.000 \
\text { Resichul Entar } & 11 & 0.1898 & 0.0173 & \
\text { Total } & 12 & 2.5060 & &
\end{array}
\end{array}$$
-{Oil Quality and Price Narrative} Determine the least squares regression line.

Accepted Answer

The answer of Oil Quality and Price
Quality of oil is...

Question 14

Wayne Newton Concert
At a recent Wayne Newton concert,a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year.The following data were collected:
 $$\begin{array}{l}
\begin{array} { | l | c c c c c c c c c c| } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number af Concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}\\
\begin{array} { | l | c c c c c c c c c c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number af Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}
\end{array}$$ An Excel output follows: 
-{Oil Quality and Price Narrative} Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (10 years)and same confidence level? Why?

Accepted Answer

The answer of Wayne Newton Concert
At a recent Wayne Newton...

Question 15

Movie Revenues
A financier whose specialty is investing in movie productions has observed that,in general,movies with "big-name" stars seem to generate more revenue than those movies whose stars are less well known.To examine his belief he records the gross revenue and the payment (in $ millions)given to the two highest-paid performers in the movie for ten recently released movies.
 $$\begin{array} { | c | c | c | } 
\hline \text { Movie } & \begin{array} { c } 
\text { Cost of Twa Highest Paid } \
\text { Perfarmers (\$mil) }
\end{array} & \begin{array} { c } 
\text { Grass Revenue } \
( \mathbf { \$ m i l } )
\end{array} \
\hline 1 & 5.3 & 48 \
2 & 7.2 & 65 \
3 & 1.3 & 18 \
4 & 1.8 & 20 \
5 & 3.5 & 31 \
6 & 2.6 & 26 \
7 & 8.0 & 73 \
8 & 2.4 & 23 \
9 & 4.5 & 39 \
10 & 0.7 & 58 \
\hline
\end{array}$$
-{Cost of Books Narrative} Estimate with 90% confidence the average selling price of all books with 900 pages.

Accepted Answer

The answer of Movie Revenues
A financier whose specialty is investing...

Question 16

Trivia Games & Education
An ardent fan of television game shows has observed that,in general,the more educated the contestant,the less money he or she wins.To test her belief she gathers data about the last eight winners of her favorite game show.She records their winnings in dollars and the number of years of education.The results are as follows.
 $$\begin{array} { | c | c | c | } 
\hline \text { Contestant } & \text { Years of Education } & \text { Winnings } \
\hline 1 & 11 & 750 \
2 & 15 & 400 \
3 & 12 & 600 \
4 & 16 & 350 \
5 & 11 & 800 \
0 & 16 & 300 \
7 & 13 & 650 \
8 & 14 & 400 \
\hline
\end{array}$$
-{Trivia Games & Education Narrative} Interpret the value of the slope of the regression line.

Accepted Answer

The answer of Trivia Games & Education
An ardent fan of...

Question 17

In performing a regression analysis which of the following must be true about the distribution of the error variable?

Accepted Answer

A)  The distribution is normal with mean zero. 
B)  The errors associated with one y value are independent of errors associated with another y value. 
C)  The standard deviation is constant for each value of x. 
D)  All of these choices are true.

Question 18

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

Accepted Answer

A) True 
 B)False

Question 19

Game Show Winnings & Education
An ardent fan of television game shows has observed that,in general,the more educated the contestant,the less money he or she wins.To test her belief she gathers data about the last eight winners of her favorite game show.She records their winnings in dollars and the number of years of education.The results are as follows.
 $$\begin{array} { | c | c | c | } 
\hline \text { Contestant } & \text { Years of Education } & \text { Winnings } \
\hline 1 & 11 & 750 \
2 & 15 & 400 \
3 & 12 & 600 \
4 & 16 & 350 \
5 & 11 & 800 \
0 & 16 & 300 \
7 & 13 & 650 \
8 & 14 & 400 \
\hline
\end{array}$$
-{Game Show Winnings & Education Narrative} Calculate the Pearson correlation coefficient.What sign does it have? Why?

Accepted Answer

The answer of Game Show Winnings & Education
An ardent fan...

Question 20

If we are interested in determining whether two variables are linearly related,it is necessary to:

Accepted Answer

A)  perform the t-test of the slope $\beta$1. 
B)  perform the t-test of the coefficient of correlation $\rho$. 
C)  either a or b since they are identical. 
D)  None of these choices.

Exam 16: A: Simple Linear Regression and Correlation

There is ____________________ error in estimating a mean than in predicting an individual value.

A prediction interval is used when we want to predict a one-time occurrence for a particular value of y when the independent variable is a given x value.

The vertical spread of the data points about the regression line is measured by the y-intercept.

If cov(x,y) = 1260, $s _ { x } ^ { 2 } = 1600$ ,and $s _ { y } ^ { 2 } = 1225$ ,then the coefficient of determination is:

A zero population correlation coefficient for x and y means that there is no type of relationship whatsoever between x and y.

In performing a regression analysis which of the following must be true about the distribution of the error variable?

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

If we are interested in determining whether two variables are linearly related,it is necessary to:

Exam 16: A: Simple Linear Regression and Correlation

There is ____________________ error in estimating a mean than in predicting an individual value.

A prediction interval is used when we want to predict a one-time occurrence for a particular value of y when the independent variable is a given x value.

The vertical spread of the data points about the regression line is measured by the y-intercept.

If cov(x,y) = 1260, sx2=1600s _ { x } ^ { 2 } = 1600sx2​=1600 ,and sy2=1225s _ { y } ^ { 2 } = 1225sy2​=1225 ,then the coefficient of determination is:

A zero population correlation coefficient for x and y means that there is no type of relationship whatsoever between x and y.

In performing a regression analysis which of the following must be true about the distribution of the error variable?

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

If we are interested in determining whether two variables are linearly related,it is necessary to:

If cov(x,y) = 1260, $s _ { x } ^ { 2 } = 1600$ ,and $s _ { y } ^ { 2 } = 1225$ ,then the coefficient of determination is: