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# Four Questions: Savings Rate, Tax, Wonderlic and Compensation

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Am working on practice problems for Management Stats class. Having problems with 4 of the questions. Please Help!

Please see attachments for correct formats and Excel charts.
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(3.31, 3.39, 3.49, 3.73)

The file SavingRate contains the yields for a money market account, a one-year certificate of deposit (CD), and a five-year CD for 23 banks in the metropolitan New York area, as of May 28, 2009. For each type of account:
a. Compute the first quartile (Q1), the third quartile (Q3), and the interquartile range.
b. List the five -number summary.
c. Construct a boxplot and describe the shape.

The file Tax contains the quarterly sales tax receipts (in thousands of dollars ) submitted to the comptroller of the Village of Fair Lake for the period ending March 2009 by all 50 businesses established in the locale:

10.3 11.1 9.6 9.0 14.5
13.0 6.7 11.0 8.4 10.3
8.0 11.8 8.7 10.6 9.5
11.1 10.2 11.1 9.9 9.8
11.6 15.1 12.5 6.5 7.5
10.0 12.9 9.2 10.0 12.8
12.5 9.3 10.4 12.7 10.5
9.3 11.5 10.7 11.6 7.8
10.5 7.6 10.1 8.9 8.6

a. Compute the mean, variance, and standard deviation for this population
b. What percentage of these businesses have quarterly sales tax receipts within + 1, + 2, or + 3 standard deviations of the mean?
c. Compare your findings with what would be expected on the basis of the empirical rule. Are you surprised at the results in (b).

College football players trying out for the NFL are given the Wonderlic standardized intelligence test. The file Wonderlic contains the average Wonderlic score of football players trying out for the NFL and the graduation rate for football players at selected schools.
a. Compute the covariance
b. Compute the coefficient of correlation
c. Based on (a) and (b), what conclusions can you reach about the relationship between the average Wonderlic score and graduation rate?

The file Compensation includes the total compensation includes the total compensation (in \$) of CEOs of the large public companies in 2008.
a. Compute the mean, median, first quartile, and third quartile.
b. Compute the range, interquartile range, variance, standard deviation, and coefficient of variation.
c. Construct a boxplot. Are the data skewed? Is so, how?
d. Based on the results of (a) through (c), what conclusions can you reach concerning the total compensation (in \$millions) of CEOs?
e. Compute the correlation coefficient between compensation and the amount of bonus.
f. Compute the correlation coefficient between compensation and the change in stock price in 2008.
g. What conclusions can you reach from the results of (e) and (f)?

https://brainmass.com/statistics/quantative-analysis-of-data/four-questions-savings-rate-tax-wonderlic-compensation-523191

#### Solution Preview

(3.31, 3.39, 3.49, 3.73)

The file SavingRate contains the yields for a money market account, a one-year certificate of deposit (CD), and a five-year CD for 23 banks in the metropolitan New York area, as of May 28, 2009. For each type of account:
a. Compute the first quartile (Q1), the third quartile (Q3), and the interquartile range.
b. List the five -number summary.
c. Construct a boxplot and describe the shape.
a)First, we arrange the data in order for the one year certificate of deposite:
0.25
0.75
0.85
1.00
1.20
1.35
1.50
1.65
1.75
1.75
1.75
2.00
2.00
2.00
2.00
2.00
2.00
2.05
2.10
2.20
2.24
2.25
2.30
Q2=12th data=2.00
Q1=(6th data+7th data)/2=(1.35+1.50)/2=1.425
Q3=(17th data+18th data)/2=(2.00+2.05)/2=2.025
Interquartile range=Q3-Q1=2.025-1.425=0.60
b)Five number summary: 0.25, 1.425, 2.00, 2.025, 2.30
0.25 is an outlier since 0.25<1.425-1.5*0.60=0.525
a')first, we arrange the data in order for five year CD:
1.00
1.16
1.50
1.65
1.70
1.70
1.70
1.70
1.85
2.50
2.80
3.00
3.00
3.00
3.10
3.25
3.25
3.30
3.30
3.30
3.50
3.66
3.70
Q2=12th data=3.00
Q1=(6th data+7th data)/2=(1.70+1.70)/2=1.70
Q3=(17th data+18th data)/2=(3.25+3.30)/2=3.275
Interquartile range=Q3-Q1=3.275-1.70=1.575
b'. the five number summary is: 1.00, 1.70, 3.00, 3.275, 3.70.
c)we could have box plot for both 1 year and 5 year CD.

From the box plot, we could see that both distribution is skewed to the left.
The file Tax contains the quarterly sales tax receipts (in thousands of dollars ) submitted to the comptroller of the Village of Fair Lake for the period ending March 2009 by all 50 businesses established in the locale:
10.3 11.1 9.6 9.0 14.5
13.0 6.7 11.0 8.4 10.3
8.0 11.8 8.7 10.6 9.5
11.1 10.2 11.1 9.9 9.8
11.6 15.1 12.5 6.5 7.5
10.0 12.9 9.2 10.0 12.8
12.5 9.3 10.4 12.7 10.5
9.3 11.5 10.7 11.6 7.8
10.5 7.6 10.1 8.9 8.6
a. Compute the mean, variance, and standard deviation for this population
b. What percentage of these businesses have quarterly sales tax receipts within + 1, + 2, or + 3
standard deviations of the mean?
c. Compare your findings with what would be expected on the basis of the empirical rule. Are you surprised at the results in (b).
a. mean=(10.3+11.1+...+8.6)/50=10.28
since this is a population, variance=((10.3-10.28)^2+(11.1-10.28)^2+...+(8.6-10.28)^2)/50=4.0984
standard deviation=sqrt(4.0984)= 2.024451
b. within 1 standard deviation: from 8.256 to 12.304. there are 32 data within this range. Therefore, The percentage: 32/50=64%.
Within 2 standard deviation: from 6.231 to 14.329. there are 47 data within this range. Therefore, the percentage: 47/50=94%
Within 3 ...

#### Solution Summary

The savings rate, tax, and Wonderlic compensation is examined.

\$2.19