To find out what is the shape of the sampling distribution and why.

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 R10.1RE

(a)

To determine

To find out what is the shape of the sampling distribution and why.

(a)

Expert Solution

Answer to Problem R10.1RE

It is approximately normal.

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

It is safe to assume that the sampling distribution of p^1−p^2 is approximately normal if,

n1p1≥10,n1(1−p1)≥10,n2p2≥10,n2(1−p2)≥10 .

Thus, we have,

n1p1=100(0.80)=80≥10n1(1−p1)=100(1−0.80)=100(0.20)=20≥10n2p2=70(0.60)=42≥10n2(1−p2)=70(1−0.60)=70(0.40)=28≥10

We note that all the conditions are met, which implies that the sampling distribution of p^1−p^2 is approximately normal.

(b)

To determine

To find the mean of the sampling distribution.

(b)

Expert Solution

Answer to Problem R10.1RE

The mean is 0.20 .

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

Thus the mean is 0.20 .

(c)

To determine

To calculate and interpret the standard deviation of the sampling distribution.

(c)

Expert Solution

Answer to Problem R10.1RE

The difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

The standard deviation of p^1−p^2 is given by:

σp^1−p^2=p1(1−p1)n1+p2(1−p2)n2=0.80(1−0.80)100+0.60(1−0.60)70=0.80(0.20)100+0.60(0.40)70=0.09586

Thus, we conclude that the difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

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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 R10.1RE

(a)

To determine

To find out what is the shape of the sampling distribution and why.

(a)

Expert Solution

Answer to Problem R10.1RE

It is approximately normal.

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

It is safe to assume that the sampling distribution of p^1−p^2 is approximately normal if,

n1p1≥10,n1(1−p1)≥10,n2p2≥10,n2(1−p2)≥10 .

Thus, we have,

n1p1=100(0.80)=80≥10n1(1−p1)=100(1−0.80)=100(0.20)=20≥10n2p2=70(0.60)=42≥10n2(1−p2)=70(1−0.60)=70(0.40)=28≥10

We note that all the conditions are met, which implies that the sampling distribution of p^1−p^2 is approximately normal.

(b)

To determine

To find the mean of the sampling distribution.

(b)

Expert Solution

Answer to Problem R10.1RE

The mean is 0.20 .

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

Thus the mean is 0.20 .

(c)

To determine

To calculate and interpret the standard deviation of the sampling distribution.

(c)

Expert Solution

Answer to Problem R10.1RE

The difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

The standard deviation of p^1−p^2 is given by:

σp^1−p^2=p1(1−p1)n1+p2(1−p2)n2=0.80(1−0.80)100+0.60(1−0.60)70=0.80(0.20)100+0.60(0.40)70=0.09586

Thus, we conclude that the difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

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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 R10.1RE

(a)

To determine

To find out what is the shape of the sampling distribution and why.

(a)

Expert Solution

Answer to Problem R10.1RE

It is approximately normal.

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

It is safe to assume that the sampling distribution of p^1−p^2 is approximately normal if,

n1p1≥10,n1(1−p1)≥10,n2p2≥10,n2(1−p2)≥10 .

Thus, we have,

n1p1=100(0.80)=80≥10n1(1−p1)=100(1−0.80)=100(0.20)=20≥10n2p2=70(0.60)=42≥10n2(1−p2)=70(1−0.60)=70(0.40)=28≥10

We note that all the conditions are met, which implies that the sampling distribution of p^1−p^2 is approximately normal.

(b)

To determine

To find the mean of the sampling distribution.

(b)

Expert Solution

Answer to Problem R10.1RE

The mean is 0.20 .

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

Thus the mean is 0.20 .

(c)

To determine

To calculate and interpret the standard deviation of the sampling distribution.

(c)

Expert Solution

Answer to Problem R10.1RE

The difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

The standard deviation of p^1−p^2 is given by:

σp^1−p^2=p1(1−p1)n1+p2(1−p2)n2=0.80(1−0.80)100+0.60(1−0.60)70=0.80(0.20)100+0.60(0.40)70=0.09586

Thus, we conclude that the difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

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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 R10.1RE

(a)

To determine

To find out what is the shape of the sampling distribution and why.

(a)

Expert Solution

Answer to Problem R10.1RE

It is approximately normal.

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

It is safe to assume that the sampling distribution of p^1−p^2 is approximately normal if,

n1p1≥10,n1(1−p1)≥10,n2p2≥10,n2(1−p2)≥10 .

Thus, we have,

n1p1=100(0.80)=80≥10n1(1−p1)=100(1−0.80)=100(0.20)=20≥10n2p2=70(0.60)=42≥10n2(1−p2)=70(1−0.60)=70(0.40)=28≥10

We note that all the conditions are met, which implies that the sampling distribution of p^1−p^2 is approximately normal.

(b)

To determine

To find the mean of the sampling distribution.

(b)

Expert Solution

Answer to Problem R10.1RE

The mean is 0.20 .

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

Thus the mean is 0.20 .

(c)

To determine

To calculate and interpret the standard deviation of the sampling distribution.

(c)

Expert Solution

Answer to Problem R10.1RE

The difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

The standard deviation of p^1−p^2 is given by:

σp^1−p^2=p1(1−p1)n1+p2(1−p2)n2=0.80(1−0.80)100+0.60(1−0.60)70=0.80(0.20)100+0.60(0.40)70=0.09586

Thus, we conclude that the difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

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Answer 5

Chapter 10, Problem R10.1RE

(a)

To determine

To find out what is the shape of the sampling distribution and why.

(a)

Expert Solution

Answer to Problem R10.1RE

It is approximately normal.

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

It is safe to assume that the sampling distribution of p^1−p^2 is approximately normal if,

n1p1≥10,n1(1−p1)≥10,n2p2≥10,n2(1−p2)≥10 .

Thus, we have,

n1p1=100(0.80)=80≥10n1(1−p1)=100(1−0.80)=100(0.20)=20≥10n2p2=70(0.60)=42≥10n2(1−p2)=70(1−0.60)=70(0.40)=28≥10

We note that all the conditions are met, which implies that the sampling distribution of p^1−p^2 is approximately normal.

(b)

To determine

To find the mean of the sampling distribution.

(b)

Expert Solution

Answer to Problem R10.1RE

The mean is 0.20 .

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

Thus the mean is 0.20 .

(c)

To determine

To calculate and interpret the standard deviation of the sampling distribution.

(c)

Expert Solution

Answer to Problem R10.1RE

The difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

The standard deviation of p^1−p^2 is given by:

σp^1−p^2=p1(1−p1)n1+p2(1−p2)n2=0.80(1−0.80)100+0.60(1−0.60)70=0.80(0.20)100+0.60(0.40)70=0.09586

Thus, we conclude that the difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

Answer 6

Chapter 10, Problem R10.1RE

(a)

To determine

To find out what is the shape of the sampling distribution and why.

(a)

Expert Solution

Answer to Problem R10.1RE

It is approximately normal.

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

It is safe to assume that the sampling distribution of p^1−p^2 is approximately normal if,

n1p1≥10,n1(1−p1)≥10,n2p2≥10,n2(1−p2)≥10 .

Thus, we have,

n1p1=100(0.80)=80≥10n1(1−p1)=100(1−0.80)=100(0.20)=20≥10n2p2=70(0.60)=42≥10n2(1−p2)=70(1−0.60)=70(0.40)=28≥10

We note that all the conditions are met, which implies that the sampling distribution of p^1−p^2 is approximately normal.

Answer 7

Chapter 10, Problem R10.1RE

(a)

To determine

To find out what is the shape of the sampling distribution and why.

Answer 8

(a)

Expert Solution

Answer to Problem R10.1RE

It is approximately normal.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

It is safe to assume that the sampling distribution of p^1−p^2 is approximately normal if,

n1p1≥10,n1(1−p1)≥10,n2p2≥10,n2(1−p2)≥10 .

Thus, we have,

n1p1=100(0.80)=80≥10n1(1−p1)=100(1−0.80)=100(0.20)=20≥10n2p2=70(0.60)=42≥10n2(1−p2)=70(1−0.60)=70(0.40)=28≥10

We note that all the conditions are met, which implies that the sampling distribution of p^1−p^2 is approximately normal.

Answer 13

(b)

To determine

To find the mean of the sampling distribution.

(b)

Expert Solution

Answer to Problem R10.1RE

The mean is 0.20 .

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

Thus the mean is 0.20 .

Answer 14

(b)

To determine

To find the mean of the sampling distribution.

Answer 15

(b)

Expert Solution

Answer to Problem R10.1RE

The mean is 0.20 .

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

Thus the mean is 0.20 .

Answer 20

(c)

To determine

To calculate and interpret the standard deviation of the sampling distribution.

(c)

Expert Solution

Answer to Problem R10.1RE

The difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

The standard deviation of p^1−p^2 is given by:

σp^1−p^2=p1(1−p1)n1+p2(1−p2)n2=0.80(1−0.80)100+0.60(1−0.60)70=0.80(0.20)100+0.60(0.40)70=0.09586

Thus, we conclude that the difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

Answer 21

(c)

To determine

To calculate and interpret the standard deviation of the sampling distribution.

Answer 22

(c)

Expert Solution

Answer to Problem R10.1RE

The difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

It is given in the question that:

n1=100n2=70p1=80%=0.80p2=60%=0.60

The mean of the sampling distribution of p^1−p^2 is the difference between the proportions:

μp^1−p^2=p1−p2=0.80−0.60=0.20

The standard deviation of p^1−p^2 is given by:

σp^1−p^2=p1(1−p1)n1+p2(1−p2)n2=0.80(1−0.80)100+0.60(1−0.60)70=0.80(0.20)100+0.60(0.40)70=0.09586

Thus, we conclude that the difference between Nathan’s state and Kyle’s state in the sample proportion of cars made by the American manufacturers varies on average by 0.09586 from the mean difference 0.20 .