Find the mean difference ( M D ) , standard deviation ( s D ) ,and standard error for the difference scores ( s M D ) .

Question

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Answer 1

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 10, Problem 16CAP

1.

To determine

Find the mean difference (MD), standard deviation (sD),and standard error for the difference scores (sMD).

1.

Expert Solution

Answer to Problem 16CAP

The mean difference for the difference scoresis –0.8.

The standard deviationfor the difference scores is 2.8.

The standard errorfor the difference scores is 1.3.

Explanation of Solution

Calculations:

From the Question 15, the calculated difference scores are –4, 1, –2, –2, and 3.

The formula for sample mean difference score is,MD=∑DnD.

The formula for sample standard deviation difference score is, sD=∑(D−MD)2nD−1.

The formula for sample standard errorof difference score is, sMD=sDnD.

Where D is difference in scores, and nD is the sample size.

Mean for the difference:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 and nD=5 in mean for the difference scores formula.

MD=−4+1−2−2+35=−45=−0.8

Thus, the mean for the difference scores is –0.8.

Standard deviation for the difference scores:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 ,MD=−0.8 and nD=5 in standard deviation for the difference scores formula.

sD=(−4+0.8)2+(1+0.8)2+(−2+0.8)2+(−2+0.8)2+(3+0.8)25−1=10.24+3.24+1.44+1.44+14.444=30.84=7.7

=2.8

Thus, the standard deviation for the difference scores is 2.8.

Standard error for the difference scores:

Substitute, sD=2.8,nD=8 in standard error for the difference scores formula.

sMD=2.85=2.82.23=1.3

Thus, the standard error for the difference scores is 1.3.

2.

To determine

Sketch the shape of the distribution of mean difference scores MD±sD.

2.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 1

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sD is 2.8.

For 1 standard deviation:

MD−sD=−0.8−2.8=−3.6

MD+sD=−0.8+2.8=2.0

For two standard deviations:

MD−2sD=−0.8−(2×2.8)=−0.8−5.6=−6.4

MD+2sD=−0.8+(2×2.8)=−0.8+5.6=4.8

For three standard deviations:

MD−3sD=−0.8−(3×2.8)=−0.8−8.4=−9.2

MD+3sD=−0.8+(3×2.8)=−0.8+8.4=7.6

Thus, the standard deviation limits for the distribution are (−3.6,2.0),(−6.4,4.8) and (−9.2,7.6).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

3.

To determine

Sketch the shape of the distribution of mean difference scores MD±sMD.

3.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sMD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 2

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sMD is 1.3.

For 1 standard deviation:

MD−sMD=−0.8−1.3=−2.1

MD+sMD=−0.8+1.3=0.5

For two standard deviations:

MD−2sMD=−0.8−(2×1.3)=−0.8−2.6=−3.4

MD+2sMD=−0.8+(2×1.3)=−0.8+2.6=1.8

For three standard deviations:

MD−3sMD=−0.8−(3×1.3)=−0.8−3.9=−4.7

MD+3sMD=−0.8+(3×1.3)=−0.8+3.9=3.1

Thus, the standard deviation limits for the distribution are (−2.1,0.5),(−3.4,1.8) and (−4.7,3.1).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

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Answer 2

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 10, Problem 16CAP

1.

To determine

Find the mean difference (MD), standard deviation (sD),and standard error for the difference scores (sMD).

1.

Expert Solution

Answer to Problem 16CAP

The mean difference for the difference scoresis –0.8.

The standard deviationfor the difference scores is 2.8.

The standard errorfor the difference scores is 1.3.

Explanation of Solution

Calculations:

From the Question 15, the calculated difference scores are –4, 1, –2, –2, and 3.

The formula for sample mean difference score is,MD=∑DnD.

The formula for sample standard deviation difference score is, sD=∑(D−MD)2nD−1.

The formula for sample standard errorof difference score is, sMD=sDnD.

Where D is difference in scores, and nD is the sample size.

Mean for the difference:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 and nD=5 in mean for the difference scores formula.

MD=−4+1−2−2+35=−45=−0.8

Thus, the mean for the difference scores is –0.8.

Standard deviation for the difference scores:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 ,MD=−0.8 and nD=5 in standard deviation for the difference scores formula.

sD=(−4+0.8)2+(1+0.8)2+(−2+0.8)2+(−2+0.8)2+(3+0.8)25−1=10.24+3.24+1.44+1.44+14.444=30.84=7.7

=2.8

Thus, the standard deviation for the difference scores is 2.8.

Standard error for the difference scores:

Substitute, sD=2.8,nD=8 in standard error for the difference scores formula.

sMD=2.85=2.82.23=1.3

Thus, the standard error for the difference scores is 1.3.

2.

To determine

Sketch the shape of the distribution of mean difference scores MD±sD.

2.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 1

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sD is 2.8.

For 1 standard deviation:

MD−sD=−0.8−2.8=−3.6

MD+sD=−0.8+2.8=2.0

For two standard deviations:

MD−2sD=−0.8−(2×2.8)=−0.8−5.6=−6.4

MD+2sD=−0.8+(2×2.8)=−0.8+5.6=4.8

For three standard deviations:

MD−3sD=−0.8−(3×2.8)=−0.8−8.4=−9.2

MD+3sD=−0.8+(3×2.8)=−0.8+8.4=7.6

Thus, the standard deviation limits for the distribution are (−3.6,2.0),(−6.4,4.8) and (−9.2,7.6).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

3.

To determine

Sketch the shape of the distribution of mean difference scores MD±sMD.

3.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sMD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 2

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sMD is 1.3.

For 1 standard deviation:

MD−sMD=−0.8−1.3=−2.1

MD+sMD=−0.8+1.3=0.5

For two standard deviations:

MD−2sMD=−0.8−(2×1.3)=−0.8−2.6=−3.4

MD+2sMD=−0.8+(2×1.3)=−0.8+2.6=1.8

For three standard deviations:

MD−3sMD=−0.8−(3×1.3)=−0.8−3.9=−4.7

MD+3sMD=−0.8+(3×1.3)=−0.8+3.9=3.1

Thus, the standard deviation limits for the distribution are (−2.1,0.5),(−3.4,1.8) and (−4.7,3.1).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

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Answer 3

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 10, Problem 16CAP

1.

To determine

Find the mean difference (MD), standard deviation (sD),and standard error for the difference scores (sMD).

1.

Expert Solution

Answer to Problem 16CAP

The mean difference for the difference scoresis –0.8.

The standard deviationfor the difference scores is 2.8.

The standard errorfor the difference scores is 1.3.

Explanation of Solution

Calculations:

From the Question 15, the calculated difference scores are –4, 1, –2, –2, and 3.

The formula for sample mean difference score is,MD=∑DnD.

The formula for sample standard deviation difference score is, sD=∑(D−MD)2nD−1.

The formula for sample standard errorof difference score is, sMD=sDnD.

Where D is difference in scores, and nD is the sample size.

Mean for the difference:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 and nD=5 in mean for the difference scores formula.

MD=−4+1−2−2+35=−45=−0.8

Thus, the mean for the difference scores is –0.8.

Standard deviation for the difference scores:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 ,MD=−0.8 and nD=5 in standard deviation for the difference scores formula.

sD=(−4+0.8)2+(1+0.8)2+(−2+0.8)2+(−2+0.8)2+(3+0.8)25−1=10.24+3.24+1.44+1.44+14.444=30.84=7.7

=2.8

Thus, the standard deviation for the difference scores is 2.8.

Standard error for the difference scores:

Substitute, sD=2.8,nD=8 in standard error for the difference scores formula.

sMD=2.85=2.82.23=1.3

Thus, the standard error for the difference scores is 1.3.

2.

To determine

Sketch the shape of the distribution of mean difference scores MD±sD.

2.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 1

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sD is 2.8.

For 1 standard deviation:

MD−sD=−0.8−2.8=−3.6

MD+sD=−0.8+2.8=2.0

For two standard deviations:

MD−2sD=−0.8−(2×2.8)=−0.8−5.6=−6.4

MD+2sD=−0.8+(2×2.8)=−0.8+5.6=4.8

For three standard deviations:

MD−3sD=−0.8−(3×2.8)=−0.8−8.4=−9.2

MD+3sD=−0.8+(3×2.8)=−0.8+8.4=7.6

Thus, the standard deviation limits for the distribution are (−3.6,2.0),(−6.4,4.8) and (−9.2,7.6).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

3.

To determine

Sketch the shape of the distribution of mean difference scores MD±sMD.

3.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sMD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 2

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sMD is 1.3.

For 1 standard deviation:

MD−sMD=−0.8−1.3=−2.1

MD+sMD=−0.8+1.3=0.5

For two standard deviations:

MD−2sMD=−0.8−(2×1.3)=−0.8−2.6=−3.4

MD+2sMD=−0.8+(2×1.3)=−0.8+2.6=1.8

For three standard deviations:

MD−3sMD=−0.8−(3×1.3)=−0.8−3.9=−4.7

MD+3sMD=−0.8+(3×1.3)=−0.8+3.9=3.1

Thus, the standard deviation limits for the distribution are (−2.1,0.5),(−3.4,1.8) and (−4.7,3.1).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

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Answer 4

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 10, Problem 16CAP

1.

To determine

Find the mean difference (MD), standard deviation (sD),and standard error for the difference scores (sMD).

1.

Expert Solution

Answer to Problem 16CAP

The mean difference for the difference scoresis –0.8.

The standard deviationfor the difference scores is 2.8.

The standard errorfor the difference scores is 1.3.

Explanation of Solution

Calculations:

From the Question 15, the calculated difference scores are –4, 1, –2, –2, and 3.

The formula for sample mean difference score is,MD=∑DnD.

The formula for sample standard deviation difference score is, sD=∑(D−MD)2nD−1.

The formula for sample standard errorof difference score is, sMD=sDnD.

Where D is difference in scores, and nD is the sample size.

Mean for the difference:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 and nD=5 in mean for the difference scores formula.

MD=−4+1−2−2+35=−45=−0.8

Thus, the mean for the difference scores is –0.8.

Standard deviation for the difference scores:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 ,MD=−0.8 and nD=5 in standard deviation for the difference scores formula.

sD=(−4+0.8)2+(1+0.8)2+(−2+0.8)2+(−2+0.8)2+(3+0.8)25−1=10.24+3.24+1.44+1.44+14.444=30.84=7.7

=2.8

Thus, the standard deviation for the difference scores is 2.8.

Standard error for the difference scores:

Substitute, sD=2.8,nD=8 in standard error for the difference scores formula.

sMD=2.85=2.82.23=1.3

Thus, the standard error for the difference scores is 1.3.

2.

To determine

Sketch the shape of the distribution of mean difference scores MD±sD.

2.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 1

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sD is 2.8.

For 1 standard deviation:

MD−sD=−0.8−2.8=−3.6

MD+sD=−0.8+2.8=2.0

For two standard deviations:

MD−2sD=−0.8−(2×2.8)=−0.8−5.6=−6.4

MD+2sD=−0.8+(2×2.8)=−0.8+5.6=4.8

For three standard deviations:

MD−3sD=−0.8−(3×2.8)=−0.8−8.4=−9.2

MD+3sD=−0.8+(3×2.8)=−0.8+8.4=7.6

Thus, the standard deviation limits for the distribution are (−3.6,2.0),(−6.4,4.8) and (−9.2,7.6).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

3.

To determine

Sketch the shape of the distribution of mean difference scores MD±sMD.

3.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sMD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 2

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sMD is 1.3.

For 1 standard deviation:

MD−sMD=−0.8−1.3=−2.1

MD+sMD=−0.8+1.3=0.5

For two standard deviations:

MD−2sMD=−0.8−(2×1.3)=−0.8−2.6=−3.4

MD+2sMD=−0.8+(2×1.3)=−0.8+2.6=1.8

For three standard deviations:

MD−3sMD=−0.8−(3×1.3)=−0.8−3.9=−4.7

MD+3sMD=−0.8+(3×1.3)=−0.8+3.9=3.1

Thus, the standard deviation limits for the distribution are (−2.1,0.5),(−3.4,1.8) and (−4.7,3.1).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

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Answer 5

Chapter 10, Problem 16CAP

1.

To determine

Find the mean difference (MD), standard deviation (sD),and standard error for the difference scores (sMD).

1.

Expert Solution

Answer to Problem 16CAP

The mean difference for the difference scoresis –0.8.

The standard deviationfor the difference scores is 2.8.

The standard errorfor the difference scores is 1.3.

Explanation of Solution

Calculations:

From the Question 15, the calculated difference scores are –4, 1, –2, –2, and 3.

The formula for sample mean difference score is,MD=∑DnD.

The formula for sample standard deviation difference score is, sD=∑(D−MD)2nD−1.

The formula for sample standard errorof difference score is, sMD=sDnD.

Where D is difference in scores, and nD is the sample size.

Mean for the difference:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 and nD=5 in mean for the difference scores formula.

MD=−4+1−2−2+35=−45=−0.8

Thus, the mean for the difference scores is –0.8.

Standard deviation for the difference scores:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 ,MD=−0.8 and nD=5 in standard deviation for the difference scores formula.

sD=(−4+0.8)2+(1+0.8)2+(−2+0.8)2+(−2+0.8)2+(3+0.8)25−1=10.24+3.24+1.44+1.44+14.444=30.84=7.7

=2.8

Thus, the standard deviation for the difference scores is 2.8.

Standard error for the difference scores:

Substitute, sD=2.8,nD=8 in standard error for the difference scores formula.

sMD=2.85=2.82.23=1.3

Thus, the standard error for the difference scores is 1.3.

2.

To determine

Sketch the shape of the distribution of mean difference scores MD±sD.

2.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 1

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sD is 2.8.

For 1 standard deviation:

MD−sD=−0.8−2.8=−3.6

MD+sD=−0.8+2.8=2.0

For two standard deviations:

MD−2sD=−0.8−(2×2.8)=−0.8−5.6=−6.4

MD+2sD=−0.8+(2×2.8)=−0.8+5.6=4.8

For three standard deviations:

MD−3sD=−0.8−(3×2.8)=−0.8−8.4=−9.2

MD+3sD=−0.8+(3×2.8)=−0.8+8.4=7.6

Thus, the standard deviation limits for the distribution are (−3.6,2.0),(−6.4,4.8) and (−9.2,7.6).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

3.

To determine

Sketch the shape of the distribution of mean difference scores MD±sMD.

3.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sMD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 2

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sMD is 1.3.

For 1 standard deviation:

MD−sMD=−0.8−1.3=−2.1

MD+sMD=−0.8+1.3=0.5

For two standard deviations:

MD−2sMD=−0.8−(2×1.3)=−0.8−2.6=−3.4

MD+2sMD=−0.8+(2×1.3)=−0.8+2.6=1.8

For three standard deviations:

MD−3sMD=−0.8−(3×1.3)=−0.8−3.9=−4.7

MD+3sMD=−0.8+(3×1.3)=−0.8+3.9=3.1

Thus, the standard deviation limits for the distribution are (−2.1,0.5),(−3.4,1.8) and (−4.7,3.1).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

Answer 6

Chapter 10, Problem 16CAP

1.

To determine

Find the mean difference (MD), standard deviation (sD),and standard error for the difference scores (sMD).

1.

Expert Solution

Answer to Problem 16CAP

The mean difference for the difference scoresis –0.8.

The standard deviationfor the difference scores is 2.8.

The standard errorfor the difference scores is 1.3.

Explanation of Solution

Calculations:

From the Question 15, the calculated difference scores are –4, 1, –2, –2, and 3.

The formula for sample mean difference score is,MD=∑DnD.

The formula for sample standard deviation difference score is, sD=∑(D−MD)2nD−1.

The formula for sample standard errorof difference score is, sMD=sDnD.

Where D is difference in scores, and nD is the sample size.

Mean for the difference:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 and nD=5 in mean for the difference scores formula.

MD=−4+1−2−2+35=−45=−0.8

Thus, the mean for the difference scores is –0.8.

Standard deviation for the difference scores:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 ,MD=−0.8 and nD=5 in standard deviation for the difference scores formula.

sD=(−4+0.8)2+(1+0.8)2+(−2+0.8)2+(−2+0.8)2+(3+0.8)25−1=10.24+3.24+1.44+1.44+14.444=30.84=7.7

=2.8

Thus, the standard deviation for the difference scores is 2.8.

Standard error for the difference scores:

Substitute, sD=2.8,nD=8 in standard error for the difference scores formula.

sMD=2.85=2.82.23=1.3

Thus, the standard error for the difference scores is 1.3.

Answer 7

Chapter 10, Problem 16CAP

1.

To determine

Find the mean difference (MD), standard deviation (sD),and standard error for the difference scores (sMD).

Answer 8

1.

Expert Solution

Answer to Problem 16CAP

The mean difference for the difference scoresis –0.8.

The standard deviationfor the difference scores is 2.8.

The standard errorfor the difference scores is 1.3.

Answer 9

1.

Expert Solution

Answer 10

1.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Calculations:

From the Question 15, the calculated difference scores are –4, 1, –2, –2, and 3.

The formula for sample mean difference score is,MD=∑DnD.

The formula for sample standard deviation difference score is, sD=∑(D−MD)2nD−1.

The formula for sample standard errorof difference score is, sMD=sDnD.

Where D is difference in scores, and nD is the sample size.

Mean for the difference:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 and nD=5 in mean for the difference scores formula.

MD=−4+1−2−2+35=−45=−0.8

Thus, the mean for the difference scores is –0.8.

Standard deviation for the difference scores:

Substitute, the values for difference scores, –4, 1, –2, –2, 3 ,MD=−0.8 and nD=5 in standard deviation for the difference scores formula.

sD=(−4+0.8)2+(1+0.8)2+(−2+0.8)2+(−2+0.8)2+(3+0.8)25−1=10.24+3.24+1.44+1.44+14.444=30.84=7.7

=2.8

Thus, the standard deviation for the difference scores is 2.8.

Standard error for the difference scores:

Substitute, sD=2.8,nD=8 in standard error for the difference scores formula.

sMD=2.85=2.82.23=1.3

Thus, the standard error for the difference scores is 1.3.

Answer 13

2.

To determine

Sketch the shape of the distribution of mean difference scores MD±sD.

2.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 1

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sD is 2.8.

For 1 standard deviation:

MD−sD=−0.8−2.8=−3.6

MD+sD=−0.8+2.8=2.0

For two standard deviations:

MD−2sD=−0.8−(2×2.8)=−0.8−5.6=−6.4

MD+2sD=−0.8+(2×2.8)=−0.8+5.6=4.8

For three standard deviations:

MD−3sD=−0.8−(3×2.8)=−0.8−8.4=−9.2

MD+3sD=−0.8+(3×2.8)=−0.8+8.4=7.6

Thus, the standard deviation limits for the distribution are (−3.6,2.0),(−6.4,4.8) and (−9.2,7.6).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

Answer 14

2.

To determine

Sketch the shape of the distribution of mean difference scores MD±sD.

Answer 15

2.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 1

Answer 16

2.

Expert Solution

Answer 17

2.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sD is 2.8.

For 1 standard deviation:

MD−sD=−0.8−2.8=−3.6

MD+sD=−0.8+2.8=2.0

For two standard deviations:

MD−2sD=−0.8−(2×2.8)=−0.8−5.6=−6.4

MD+2sD=−0.8+(2×2.8)=−0.8+5.6=4.8

For three standard deviations:

MD−3sD=−0.8−(3×2.8)=−0.8−8.4=−9.2

MD+3sD=−0.8+(3×2.8)=−0.8+8.4=7.6

Thus, the standard deviation limits for the distribution are (−3.6,2.0),(−6.4,4.8) and (−9.2,7.6).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

Answer 20

3.

To determine

Sketch the shape of the distribution of mean difference scores MD±sMD.

3.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sMD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 2

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sMD is 1.3.

For 1 standard deviation:

MD−sMD=−0.8−1.3=−2.1

MD+sMD=−0.8+1.3=0.5

For two standard deviations:

MD−2sMD=−0.8−(2×1.3)=−0.8−2.6=−3.4

MD+2sMD=−0.8+(2×1.3)=−0.8+2.6=1.8

For three standard deviations:

MD−3sMD=−0.8−(3×1.3)=−0.8−3.9=−4.7

MD+3sMD=−0.8+(3×1.3)=−0.8+3.9=3.1

Thus, the standard deviation limits for the distribution are (−2.1,0.5),(−3.4,1.8) and (−4.7,3.1).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.

Answer 21

3.

To determine

Sketch the shape of the distribution of mean difference scores MD±sMD.

Answer 22

3.

Expert Solution

Answer to Problem 16CAP

The shape of the distribution of mean difference scores MD±sMD is,

Statistics for the Behavioral Sciences, Chapter 10, Problem 16CAP , additional homework tip 2

Answer 23

3.

Expert Solution

Answer 24

3.

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Calculation:

The value of MD is –0.8 and the value of sMD is 1.3.

For 1 standard deviation:

MD−sMD=−0.8−1.3=−2.1

MD+sMD=−0.8+1.3=0.5

For two standard deviations:

MD−2sMD=−0.8−(2×1.3)=−0.8−2.6=−3.4

MD+2sMD=−0.8+(2×1.3)=−0.8+2.6=1.8

For three standard deviations:

MD−3sMD=−0.8−(3×1.3)=−0.8−3.9=−4.7

MD+3sMD=−0.8+(3×1.3)=−0.8+3.9=3.1

Thus, the standard deviation limits for the distribution are (−2.1,0.5),(−3.4,1.8) and (−4.7,3.1).

Sketch of Graph:

Step by step procedure for sketching the graph:

The mean of the distribution is taken in the centre of the graph.
The one standard deviation limits are taken on either side of the mean.
The two standard deviations limits are taken on either side of one standard deviation limits.
The three standard deviations limits are taken on either side of two standard deviations limits.
Draw the graph.