Question 1

A random sample of 60 students in the business statistics course answered a survey on the average number of hours they spent on statistics each week.Unfortunately,the original data were lost and all that remains is the frequency table below.From these data,calculate the estimated sample standard deviation.$\begin{array}{cccccc}
\text { Class } & \text { Hrs } & \text { N } & \text { Midpt } & \text { fM } \
1 & 0-3 & 18 & 1.5 & 27 \
2 & 4-7 & 16 & 5.5 & 88 \
3 & 8-11 & 14 & 9.5 & 133 \
4 & 12-15 & 10 & 13.5 & 135 \
5 & 16-19 &\underline { 2} & 17.5 & \underline {35}\
&&60&&418\
\end{array}$

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Question 2

In a study of the factors that affect success in economics,data were collected for 8 business students.Scores on a calculus placement test are given with economics final exam scores.The data are below: $\begin{array} { | l | l | } \hline \begin{array} { l } \text { Calculus } \ \text { Placement Score } \end{array} & \begin{array} { l } \text { Exam Final } \ \text { Score } \end{array} \ \hline 17 & 73 \ \hline 21 & 66 \ \hline 11 & 64 \ \hline 16 & 61 \ \hline 15 & 70 \ \hline 11 & 71 \ \hline 24 & 90 \ \hline 27 & 68 \ \hline \end{array}$ It can be shown that for these data: $\bar{X}=17.75, \quad \bar{y}=70.38, \quad \sum_{i=1}^{8}\left(x_{i}-\bar{x}\right)^{2}=237.50$ $\sum_{i=1}^{8}\left(y_{i}-\bar{y}\right)^{2}=545.875, \quad \sum_{i=1}^{8}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=140.75$ Calculate b₁.

Accepted Answer

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Question 3

Researchers wish to study fuel consumption rates based on speed.The data from 10 cars are below. $\begin{array} { | l | l | } 
\hline \text { Speed } & \text { Miles/Gallon } \
\hline 15 & 14 \
\hline 23 & 17 \
\hline 30 & 20 \
\hline 35 & 24 \
\hline 42 & 26 \
\hline 45 & 23 \
\hline 50 & 18 \
\hline 54 & 15 \
\hline 60 & 11 \
\hline 65 & 10 \
\hline
\end{array}$
It can be shown that for these data: $\bar{X}=41.9, \quad \bar{y}=17.8, \quad \sum_{i=1}^{10}\left(x_{i}-\bar{x}\right)^{2}=2352.9$
$\sum_{i=1}^{10}\left(y_{i}-\bar{y}\right)^{2}=267.6, \quad \sum_{i=1}^{10}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=-270.2$
Calculate the sample correlation coefficient.
A)0.12
B)-0.12
C)-0.36
D)-0.34
E)0.34

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Question 4

A random sample of 60 students in the business statistics course answered a survey on the average number of hours they spent on statistics each week.Unfortunately,the original data were lost and all that remains is the frequency table below.From these data,calculate the estimated sample mean.
$\begin{array} { c c r } 
\text { Class } & \text { Hrs } & \mathrm { N } \
1 & 0 - 3 & 18 \
2 & 4 - 7 & 16 \
3 & 8 - 11 & 14 \
4 & 12 - 15 & 10 \
5 & 16 - 19 & 2
\end{array}$

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Question 5

The geometric mean growth rate of sales for used cars in a geographic area from 2005 to 2009 was 16.42 percent.Annual sales in 2005 were $14.2 million.Find the ending value of sales after this four-year period.

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Question 6

The marketing research department of a company was asked to respond to the CEO's question about the average age of consumers of the company's most profitable product.From survey data gathered two years ago,the researchers found the following table.Calculate the average age to give to the CEO.
$\begin{array} { | c | r | } 
\hline \text { Midpt of Age Class } & \text { N } \
\hline 17.5 & \
\hline 23.5 & 65 \
\hline 29.5 & 100 \
\hline 35.5 & 220 \
\hline 41.5 & 250 \
\hline 52.5 & 120 \
\hline
\end{array}$

Accepted Answer

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Question 7

Researchers wish to study fuel consumption rates based on speed.The data from 10 cars are below: $\begin{array} { | l | l | } \hline \text { Speed } & \text { Miles/Gallon } \ \hline 15 & 14 \ \hline 23 & 17 \ \hline 30 & 20 \ \hline 35 & 24 \ \hline 42 & 26 \ \hline 45 & 23 \ \hline 50 & 18 \ \hline 54 & 15 \ \hline 60 & 11 \ \hline 65 & 10 \ \hline \end{array}$ It can be shown that for these data: $\bar{X}=41.9, \quad \bar{y}=17.8, \quad \sum_{i=1}^{10}\left(x_{i}-\bar{x}\right)^{2}=2352.9$ $\sum_{i=1}^{10}\left(y_{i}-\bar{y}\right)^{2}=267.6, \quad \sum_{i=1}^{10}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=-270.2$ Calculate b₁.

Accepted Answer

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Question 8

Find the weighted mean per capita income for the following random sample of six cities in the Midwest.
$\begin{array}{|l|r|r|}
\hline \text { City } & \text { Population }&\text { Per Capita Income } \
\hline \text { A } & 540,000 &\$26,338  \
\hline \text { B } & 1,250,000 &\$ 28,455  \
\hline \text { C } & 325,000 &\$  36,574 \
\hline \text { D } & 2,461,000 &\$  33,690 \
\hline \text { E } & 845,000&\$  31,998  \
\hline \text { F } & 620,000&\$ 29,442 \
\hline
\end{array}$

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Question 9

From the following table of values and corresponding sample sizes,calculate the weighted mean.

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Question 10

In a study of the factors that affect success in economics,data were collected for 8 business students.Scores on a calculus placement test are given with economics final exam scores.The data are below: $\begin{array} { | l | l | } 
\hline \begin{array} { l } 
\text { Calculus } \
\text { Placement Score }
\end{array} & \begin{array} { l } 
\text { Exam Final } \
\text { Score }
\end{array} \
\hline 17 & 73 \
\hline 21 & 66 \
\hline 11 & 64 \
\hline 16 & 61 \
\hline 15 & 70 \
\hline 11 & 71 \
\hline 24 & 90 \
\hline 27 & 68 \
\hline
\end{array}$
It can be shown that for these data: $\bar{X}=17.75, \quad \bar{y}=70.38, \quad \sum_{i=1}^{8}\left(x_{i}-\bar{x}\right)^{2}=237.50$
$\sum_{i=1}^{8}\left(y_{i}-\bar{y}\right)^{2}=545.875, \quad \sum_{i=1}^{8}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=140.75$
Calculate the sample covariance.
A)17.59
B)7.93
C)2.00
D)33.93
E)20.11

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Question 11

Using grouped data of 14 classes with a sample mean of 51 and a sample variance of 6.42,calculate the group sampled standard deviation.

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Question 12

A real estate appraiser is gathering housing sales data by street in the neighborhood in preparation for his next job.Listed below are the six streets and the average sales price and the houses sold in the last 12 months.Calculate the mean sales price for the neighborhood.
$\begin{array} { | l | c | r | } 
\hline \text { Street } & \text { Avg Sales Price } & \mathrm { N } \
\hline \text { Elm } & 159,999 & 1 \
\hline \text { Maple } & 210,998 & 6 \
\hline \text { Oak } & 185,000 & 4 \
\hline \text { Pine } & 202,632 & 4 \
\hline \text { Rose } & 175,500 & 5 \
\hline \text { Petunia } & 352,941 & 3 \
\hline
\end{array}$

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Question 13

In an analysis of the relationship between the average weekly temperature in a major city and the per person consumption of ice cream (pints),a least squares line is defined by the equation 5.72 + .004x.Predict the average amount of ice cream consumed when it is 50° outside.

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Question 14

An initial investment of $10,000 is observed over 3 years with a geometric mean return at the end of year 3 of 0.512.Determine the value of the investment after 3 years.

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Question 15

Joe Smith's IRA at the end of 2007 had a value of $1.2 million.With a rate of return of -29.75 percent in 2008 and a rate of return of 2.98 percent in 2009,calculate the geometric mean rate of return for the two-year period.

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Question 16

An initial investment of $10,000 has a value of $7,382 at the end of year 1,a rate of return of 62.43 percent for year 2,and a geometric mean return at the end of year 3 of 0.512.Determine the rate of return for the third year.

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Question 17

An initial investment of $10,000 has a value of $7,382 at the end of year 1.What is the rate of return for the first year?

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Question 18

In a study of the factors that affect success in economics,data were collected for 8 business students.Scores on a calculus placement test are given with economics final exam scores.The data are below. $\begin{array} { | l | l | } 
\hline \begin{array} { l } 
\text { Calculus } \
\text { Placement Score }
\end{array} & \begin{array} { l } 
\text { Exam Final } \
\text { Score }
\end{array} \
\hline 17 & 73 \
\hline 21 & 66 \
\hline 11 & 64 \
\hline 16 & 61 \
\hline 15 & 70 \
\hline 11 & 71 \
\hline 24 & 90 \
\hline 27 & 68 \
\hline
\end{array}$
It can be shown that for these data: $\bar{X}=17.75, \quad \bar{y}=70.38, \quad \sum_{i=1}^{8}\left(x_{i}-\bar{x}\right)^{2}=237.50$
$\sum_{i=1}^{8}\left(y_{i}-\bar{y}\right)^{2}=545.875, \quad \sum_{i=1}^{8}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=140.75$
Calculate the sample correlation coefficient.
A)0.15
B)0.11
C)0.39
D)-0.39
E)-0.11

Accepted Answer

The formula for the sample correlation coefficient is: 
\begin{align*}
r &= \frac{\sum_{i=1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sqrt{\sum_{i=1}^{n}(x_{i}-\bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_{i}-\bar{y})^2}}\
&= \frac{140.75}{\sqrt{237.50}\sqrt{545.875}}\
&\approx 0.39
\end{align*}
Therefore, the correct answer is (C) 0.39. This indicates a moderately positive correlation between calculus placement scores and economics final exam scores.

Question 19

Researchers wish to study fuel consumption rates based on speed.The data from 10 cars are below: $\begin{array} { | l | l | } 
\hline \text { Speed } & \text { Miles/Gallon } \
\hline 15 & 14 \
\hline 23 & 17 \
\hline 30 & 20 \
\hline 35 & 24 \
\hline 42 & 26 \
\hline 45 & 23 \
\hline 50 & 18 \
\hline 54 & 15 \
\hline 60 & 11 \
\hline 65 & 10 \
\hline
\end{array}$
It can be shown that for these data: $\bar{X}=41.9, \quad \bar{y}=17.8, \quad \sum_{i=1}^{10}\left(x_{i}-\bar{x}\right)^{2}=2352.9$
$\sum_{i=1}^{10}\left(y_{i}-\bar{y}\right)^{2}=267.6, \quad \sum_{i=1}^{10}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=-270.2$
Calculate the sample covariance.
A)-270.2
B)-30.02
C)-27.02
D)-74.58
E)-82.86

Accepted Answer

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Question 20

In a study of employee stock ownership plans,data wee collected at seven companies on satisfaction with the plan and the amount of organization commitment. $\begin{array} { | l | l | } \hline \text { Satisfaction } & \text { Commitment } \ \hline 5.05 & 5.37 \ \hline 4.12 & 4.49 \ \hline 5.39 & 5.42 \ \hline 4.17 & 4.45 \ \hline 4.00 & 4.24 \ \hline 4.49 & 5.34 \ \hline 5.40 & 5.62 \ \hline \end{array}$ It can be shown that for these data: $\bar{X}=4.66, \quad \bar{y}=4.99, \quad \sum_{i=1}^{7}\left(x_{i}-\bar{x}\right)^{2}=2.23$ $\sum_{i=1}^{7}\left(y_{i}-\bar{y}\right)^{2}=1.95, \quad \sum_{i=1}^{7}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)=1.898$ Calculate b₁.

Accepted Answer

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Quiz 3: Descriptive Statistics: Numerical Methods

The geometric mean growth rate of sales for used cars in a geographic area from 2005 to 2009 was 16.42 percent.Annual sales in 2005 were $14.2 million.Find the ending value of sales after this four-year period.

From the following table of values and corresponding sample sizes,calculate the weighted mean.

Using grouped data of 14 classes with a sample mean of 51 and a sample variance of 6.42,calculate the group sampled standard deviation.

In an analysis of the relationship between the average weekly temperature in a major city and the per person consumption of ice cream (pints),a least squares line is defined by the equation 5.72 + .004x.Predict the average amount of ice cream consumed when it is 50° outside.

An initial investment of $10,000 is observed over 3 years with a geometric mean return at the end of year 3 of 0.512.Determine the value of the investment after 3 years.

Joe Smith's IRA at the end of 2007 had a value of $1.2 million.With a rate of return of -29.75 percent in 2008 and a rate of return of 2.98 percent in 2009,calculate the geometric mean rate of return for the two-year period.

An initial investment of $10,000 has a value of $7,382 at the end of year 1,a rate of return of 62.43 percent for year 2,and a geometric mean return at the end of year 3 of 0.512.Determine the rate of return for the third year.

An initial investment of $10,000 has a value of $7,382 at the end of year 1.What is the rate of return for the first year?