The reason for prefer the t procedure to the z procedure for inference about population mean .

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 20, Problem 20.15CYS

To determine

To find: The reason for prefer the t procedure to the z procedure for inference about population mean.

Expert Solution & Answer

Answer to Problem 20.15CYS

Option (b)

Explanation of Solution

Reason for the correct option:

Prefer the t procedures to the z procedures for inference about a population mean because z procedures require that the population standard deviation is known but the t procedures are not required.

Reason for the incorrect answer:

For both test procedures, the data or observations considered as simple random sample from the population and the observations are from a normal population. Therefore,

Option (a) and Option (c) are incorrect.

Therefore, the correct option is (b), “z requires that you know the population standard deviation σ , while t does not”.

Statistics Concept Introduction

Introduction:

Conditions for inference about a one-sample t test:

Simple random sample from the population.
Observations are from a normal population.

Conditions for inference about a one-sample z test:

Simple random sample from the population.
Observations are from a normal population.
Population standard deviation is known.

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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 20, Problem 20.15CYS

To determine

To find: The reason for prefer the t procedure to the z procedure for inference about population mean.

Expert Solution & Answer

Answer to Problem 20.15CYS

Option (b)

Explanation of Solution

Reason for the correct option:

Prefer the t procedures to the z procedures for inference about a population mean because z procedures require that the population standard deviation is known but the t procedures are not required.

Reason for the incorrect answer:

For both test procedures, the data or observations considered as simple random sample from the population and the observations are from a normal population. Therefore,

Option (a) and Option (c) are incorrect.

Therefore, the correct option is (b), “z requires that you know the population standard deviation σ , while t does not”.

Statistics Concept Introduction

Introduction:

Conditions for inference about a one-sample t test:

Simple random sample from the population.
Observations are from a normal population.

Conditions for inference about a one-sample z test:

Simple random sample from the population.
Observations are from a normal population.
Population standard deviation is known.

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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 20, Problem 20.15CYS

To determine

To find: The reason for prefer the t procedure to the z procedure for inference about population mean.

Expert Solution & Answer

Answer to Problem 20.15CYS

Option (b)

Explanation of Solution

Reason for the correct option:

Prefer the t procedures to the z procedures for inference about a population mean because z procedures require that the population standard deviation is known but the t procedures are not required.

Reason for the incorrect answer:

For both test procedures, the data or observations considered as simple random sample from the population and the observations are from a normal population. Therefore,

Option (a) and Option (c) are incorrect.

Therefore, the correct option is (b), “z requires that you know the population standard deviation σ , while t does not”.

Statistics Concept Introduction

Introduction:

Conditions for inference about a one-sample t test:

Simple random sample from the population.
Observations are from a normal population.

Conditions for inference about a one-sample z test:

Simple random sample from the population.
Observations are from a normal population.
Population standard deviation is known.

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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 20, Problem 20.15CYS

To determine

To find: The reason for prefer the t procedure to the z procedure for inference about population mean.

Expert Solution & Answer

Answer to Problem 20.15CYS

Option (b)

Explanation of Solution

Reason for the correct option:

Prefer the t procedures to the z procedures for inference about a population mean because z procedures require that the population standard deviation is known but the t procedures are not required.

Reason for the incorrect answer:

For both test procedures, the data or observations considered as simple random sample from the population and the observations are from a normal population. Therefore,

Option (a) and Option (c) are incorrect.

Therefore, the correct option is (b), “z requires that you know the population standard deviation σ , while t does not”.

Statistics Concept Introduction

Introduction:

Conditions for inference about a one-sample t test:

Simple random sample from the population.
Observations are from a normal population.

Conditions for inference about a one-sample z test:

Simple random sample from the population.
Observations are from a normal population.
Population standard deviation is known.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 20, Problem 20.15CYS

To determine

To find: The reason for prefer the t procedure to the z procedure for inference about population mean.

Expert Solution & Answer

Answer to Problem 20.15CYS

Option (b)

Explanation of Solution

Reason for the correct option:

Prefer the t procedures to the z procedures for inference about a population mean because z procedures require that the population standard deviation is known but the t procedures are not required.

Reason for the incorrect answer:

For both test procedures, the data or observations considered as simple random sample from the population and the observations are from a normal population. Therefore,

Option (a) and Option (c) are incorrect.

Therefore, the correct option is (b), “z requires that you know the population standard deviation σ , while t does not”.

Statistics Concept Introduction

Introduction:

Conditions for inference about a one-sample t test:

Simple random sample from the population.
Observations are from a normal population.

Conditions for inference about a one-sample z test:

Simple random sample from the population.
Observations are from a normal population.
Population standard deviation is known.

Answer 6

Chapter 20, Problem 20.15CYS

To determine

To find: The reason for prefer the t procedure to the z procedure for inference about population mean.

Expert Solution & Answer

Answer to Problem 20.15CYS

Option (b)

Explanation of Solution

Reason for the correct option:

Prefer the t procedures to the z procedures for inference about a population mean because z procedures require that the population standard deviation is known but the t procedures are not required.

Reason for the incorrect answer:

For both test procedures, the data or observations considered as simple random sample from the population and the observations are from a normal population. Therefore,

Option (a) and Option (c) are incorrect.

Therefore, the correct option is (b), “z requires that you know the population standard deviation σ , while t does not”.

Statistics Concept Introduction

Introduction:

Conditions for inference about a one-sample t test:

Simple random sample from the population.
Observations are from a normal population.

Conditions for inference about a one-sample z test:

Simple random sample from the population.
Observations are from a normal population.
Population standard deviation is known.

Answer 7

Chapter 20, Problem 20.15CYS

To determine

To find: The reason for prefer the t procedure to the z procedure for inference about population mean.

Answer 8

Expert Solution & Answer

Answer to Problem 20.15CYS

Option (b)

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Reason for the correct option:

Prefer the t procedures to the z procedures for inference about a population mean because z procedures require that the population standard deviation is known but the t procedures are not required.

Reason for the incorrect answer:

For both test procedures, the data or observations considered as simple random sample from the population and the observations are from a normal population. Therefore,

Option (a) and Option (c) are incorrect.

Therefore, the correct option is (b), “z requires that you know the population standard deviation σ , while t does not”.