Understandable Statistics: Concepts and Methods
Understandable Statistics: Concepts and Methods
12th Edition
ISBN: 9781337119917
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 3.2, Problem 18P

a.

To determine

Find the values x,x2,y, and y2 using calculator.

a.

Expert Solution
Check Mark

Answer to Problem 18P

The values of x=284.95_ and x2=7,046.80_.

The values of y=421.5_ and y2=14,562.29_.

Explanation of Solution

Step-by-step procedure to verify x and x2 using Ti83 calculator is given below:

  • Press STAT.
  • Select Edit.
  • Enter the values in L1.
  • Press STAT and Choose CALC.
  • Select 1-Var Stats.
  • To select the variable L1, Press 2-nd, and then press 1.
  • Press Enter.

Output obtained using the Ti83 calculator is given below:

Understandable Statistics: Concepts and Methods, Chapter 3.2, Problem 18P , additional homework tip  1

From the output, the values of x=284.95 and x2=7,046.80.

Step-by-step procedure to verify y and y2 using Ti83 calculator is given below:

  • Press STAT.
  • Select Edit.
  • Enter the values in L2.
  • Press STAT and Choose CALC.
  • Select 1-Var Stats.
  • To select the variable L2, Press 2-nd, and then press 2.
  • Press Enter.

Output obtained using the Ti83 calculator is given below:

Understandable Statistics: Concepts and Methods, Chapter 3.2, Problem 18P , additional homework tip  2

From the output, the values of y=421.5 and y2=14,562.29.

b.

To determine

Find the sample mean, variance, and standard deviation for x and y using the computation formula.

b.

Expert Solution
Check Mark

Answer to Problem 18P

The values of sample mean, variance, and standard deviation for x using the computation formula is 20.35, 96 and 9.79.

The values of sample mean, variance, and standard deviation for y using the computation formula is 28.1, 194 and 13.93.

Explanation of Solution

The sample variance using the computation formula is as follows:

s2=x2(x)2nn1

Where, x¯ is the mean, n is the number of values in the data, and x is the values in the data.

The sample standard deviation using the computation formula is as follows:

s=x2(x)2nn1

Where, x¯ is the mean, n is the number of values in the data, and x is the values in the data.

The sample mean for x is obtained below:

x¯=xn=284.9514=20.35

Thus, the sample mean is 20.35.

The sample variance for x using the computation formula is obtained below:

s2=7046.80(284.95)214141=96

Thus, the sample variance for x using the computation formula is 96.

The sample standard deviation for x using the computation formula is obtained below:

s=96=9.79

Thus, the sample standard deviation for x using the computation formula is 9.79.

The sample mean for y is obtained below:

y¯=yn=421.515=28.1

Thus, the sample mean is 28.1.

The sample variance for y using the computation formula is obtained below:

s2=14562.29(421.5)215151=194.1194

Thus, the sample variance for y using the computation formula is 194.

The sample standard deviation for y using the computation formula is obtained below:

s=194=13.93

Thus, the sample standard deviation for y using the computation formula is 13.93.

c.

To determine

Find the 75% Chebyshev interval around the mean for each fund.

Compare the two grids.

c.

Expert Solution
Check Mark

Answer to Problem 18P

The 75% Chebyshev interval around the mean for the Grid E is 0.77 and 39.93.

The 75% Chebyshev interval around the mean for the Grid H is 0.24 and 55.96.

Explanation of Solution

The 75% Chebyshev interval around the mean for the Grid Eis obtained below:

x¯2s=20.352(9.79)=0.77x¯+2s=20.35+2(9.79)=39.93

Thus, the 75% Chebyshev interval around the mean for the Grid E is 0.77 and 39.93.

The 75% Chebyshev interval around the mean for the Grid H is obtained below:

y¯2s=28.12(13.93)=0.24y¯+2s=28.1+2(13.93)=55.96

Thus, the 75% Chebyshev interval around the mean for the Grid H is 0.24 and 55.96.

From the result, it is observed that the 75% Chebyshev interval around the mean for the Grid H is wider when compared to the Grid E.

d.

To determine

Find and compare the coefficient of variation for x and y.

d.

Expert Solution
Check Mark

Answer to Problem 18P

The coefficient of variation for x is 48%.

The coefficient of variation for y is 50%.

Explanation of Solution

The formula for the coefficient of variation is as follows:

CV=sx¯×100%

Where, s is the sample standard deviation and x¯ is the sample mean.

The coefficient of variation for x is obtained below:

CV=9.7920.35×100%=48%

Thus, the coefficient of variation for x is 48%.

The coefficient of variation for y is obtained below:

CV=13.9328.1×100%=50%

Thus, the coefficient of variation for y is 50%.

From the results, the coefficient of variation for the Grid E is less when compared to the coefficient of variation for the Grid H. Hence, the Grid H has more buried artifacts.

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Understandable Statistics: Concepts and Methods

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