The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following: a. An increase in the difference between the sample mean and the original population mean. b. An increase in the population standard deviation. c. An increase in the number of scores in the sample.

Question

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Answer 1

Textbook Question

Chapter 8, Problem 1P

The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following:

a. An increase in the difference between the sample mean and the original population mean.

b. An increase in the population standard deviation.

c. An increase in the number of scores in the sample.

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 + ...

a.

Expert Solution

To determine

The effect of z-score on increase in difference between sample mean and original population mean.

Answer to Problem 1P

The z-score increases with the increase in difference between sample mean and original population mean.

Explanation of Solution

The z-score is,

z-value=Mean differenceStandard error

The z-score is directly proportional to the mean difference. So, increase in mean difference increases the z-value.

b.

Expert Solution

To determine

The effect on z-value of an increase in the population standard deviation

Answer to Problem 1P

The z-value decreases with an increase in the population standard deviation

Explanation of Solution

Justification:

z-value=mean differencestandard error×n

The z-value is inversely proportional to the standard deviation. So, increasing the standard deviation, then z-score decreases.

c.

Expert Solution

To determine

The effect on z-value of an increase in the number of scores in sample.

Answer to Problem 1P

The z-value decreases with an increase in the number of scores in sample.

Explanation of Solution

Increasing the number of z-scores in sample, decrease z.

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Answer 2

Textbook Question

Chapter 8, Problem 1P

The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following:

a. An increase in the difference between the sample mean and the original population mean.

b. An increase in the population standard deviation.

c. An increase in the number of scores in the sample.

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 + ...

a.

Expert Solution

To determine

The effect of z-score on increase in difference between sample mean and original population mean.

Answer to Problem 1P

The z-score increases with the increase in difference between sample mean and original population mean.

Explanation of Solution

The z-score is,

z-value=Mean differenceStandard error

The z-score is directly proportional to the mean difference. So, increase in mean difference increases the z-value.

b.

Expert Solution

To determine

The effect on z-value of an increase in the population standard deviation

Answer to Problem 1P

The z-value decreases with an increase in the population standard deviation

Explanation of Solution

Justification:

z-value=mean differencestandard error×n

The z-value is inversely proportional to the standard deviation. So, increasing the standard deviation, then z-score decreases.

c.

Expert Solution

To determine

The effect on z-value of an increase in the number of scores in sample.

Answer to Problem 1P

The z-value decreases with an increase in the number of scores in sample.

Explanation of Solution

Increasing the number of z-scores in sample, decrease z.

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Answer 3

Textbook Question

Chapter 8, Problem 1P

The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following:

a. An increase in the difference between the sample mean and the original population mean.

b. An increase in the population standard deviation.

c. An increase in the number of scores in the sample.

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 + ...

a.

Expert Solution

To determine

The effect of z-score on increase in difference between sample mean and original population mean.

Answer to Problem 1P

The z-score increases with the increase in difference between sample mean and original population mean.

Explanation of Solution

The z-score is,

z-value=Mean differenceStandard error

The z-score is directly proportional to the mean difference. So, increase in mean difference increases the z-value.

b.

Expert Solution

To determine

The effect on z-value of an increase in the population standard deviation

Answer to Problem 1P

The z-value decreases with an increase in the population standard deviation

Explanation of Solution

Justification:

z-value=mean differencestandard error×n

The z-value is inversely proportional to the standard deviation. So, increasing the standard deviation, then z-score decreases.

c.

Expert Solution

To determine

The effect on z-value of an increase in the number of scores in sample.

Answer to Problem 1P

The z-value decreases with an increase in the number of scores in sample.

Explanation of Solution

Increasing the number of z-scores in sample, decrease z.

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Answer 4

Textbook Question

Chapter 8, Problem 1P

The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following:

a. An increase in the difference between the sample mean and the original population mean.

b. An increase in the population standard deviation.

c. An increase in the number of scores in the sample.

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 + ...

a.

Expert Solution

To determine

The effect of z-score on increase in difference between sample mean and original population mean.

Answer to Problem 1P

The z-score increases with the increase in difference between sample mean and original population mean.

Explanation of Solution

The z-score is,

z-value=Mean differenceStandard error

The z-score is directly proportional to the mean difference. So, increase in mean difference increases the z-value.

b.

Expert Solution

To determine

The effect on z-value of an increase in the population standard deviation

Answer to Problem 1P

The z-value decreases with an increase in the population standard deviation

Explanation of Solution

Justification:

z-value=mean differencestandard error×n

The z-value is inversely proportional to the standard deviation. So, increasing the standard deviation, then z-score decreases.

c.

Expert Solution

To determine

The effect on z-value of an increase in the number of scores in sample.

Answer to Problem 1P

The z-value decreases with an increase in the number of scores in sample.

Explanation of Solution

Increasing the number of z-scores in sample, decrease z.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

The effect of z-score on increase in difference between sample mean and original population mean.

Answer to Problem 1P

The z-score increases with the increase in difference between sample mean and original population mean.

Explanation of Solution

The z-score is,

z-value=Mean differenceStandard error

The z-score is directly proportional to the mean difference. So, increase in mean difference increases the z-value.

b.

Expert Solution

To determine

The effect on z-value of an increase in the population standard deviation

Answer to Problem 1P

The z-value decreases with an increase in the population standard deviation

Explanation of Solution

Justification:

z-value=mean differencestandard error×n

The z-value is inversely proportional to the standard deviation. So, increasing the standard deviation, then z-score decreases.

c.

Expert Solution

To determine

The effect on z-value of an increase in the number of scores in sample.

Answer to Problem 1P

The z-value decreases with an increase in the number of scores in sample.

Explanation of Solution

Increasing the number of z-scores in sample, decrease z.

Answer 8

a.

Expert Solution

To determine

The effect of z-score on increase in difference between sample mean and original population mean.

Answer to Problem 1P

The z-score increases with the increase in difference between sample mean and original population mean.

Explanation of Solution

The z-score is,

z-value=Mean differenceStandard error

The z-score is directly proportional to the mean difference. So, increase in mean difference increases the z-value.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

The effect of z-score on increase in difference between sample mean and original population mean.

Answer 13

Answer to Problem 1P

The z-score increases with the increase in difference between sample mean and original population mean.

Answer 14

Explanation of Solution

The z-score is,

z-value=Mean differenceStandard error

The z-score is directly proportional to the mean difference. So, increase in mean difference increases the z-value.

Answer 15

b.

Expert Solution

To determine

The effect on z-value of an increase in the population standard deviation

Answer to Problem 1P

The z-value decreases with an increase in the population standard deviation

Explanation of Solution

Justification:

z-value=mean differencestandard error×n

The z-value is inversely proportional to the standard deviation. So, increasing the standard deviation, then z-score decreases.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

The effect on z-value of an increase in the population standard deviation

Answer 20

Answer to Problem 1P

The z-value decreases with an increase in the population standard deviation

Answer 21

Explanation of Solution

Justification:

z-value=mean differencestandard error×n

The z-value is inversely proportional to the standard deviation. So, increasing the standard deviation, then z-score decreases.

Answer 22

c.

Expert Solution

To determine

The effect on z-value of an increase in the number of scores in sample.

Answer to Problem 1P

The z-value decreases with an increase in the number of scores in sample.

Explanation of Solution

Increasing the number of z-scores in sample, decrease z.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

The effect on z-value of an increase in the number of scores in sample.

Answer 27

Answer to Problem 1P

The z-value decreases with an increase in the number of scores in sample.

Answer 28

Explanation of Solution

Increasing the number of z-scores in sample, decrease z.

Answer 29

Ch. 8.1 - The city school district is considering increasing...Ch. 8.1 - Prob. 2LC Ch. 8.1 - Prob. 3LC Ch. 8.1 - A researcher selects a sample of n = 16...Ch. 8.1 - A small value (near zero) for the z-score...Ch. 8.1 - Prob. 3LCA Ch. 8.2 - Prob. 1LC Ch. 8.2 - Prob. 2LC Ch. 8.2 - Prob. 3LC Ch. 8.2 - Prob. 4LC

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