The information that is needed to find whether the given mean value belongs to a statistic or parameter.

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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 11, Problem 11.1E

To determine

To explain: The information that is needed to find whether the given mean value belongs to a statistic or parameter.

Expert Solution & Answer

Explanation of Solution

Given information:

The mean score of 105.3 for the students of a specific school.

Concept used:

The whole collection or group of all the elements is known as the population. The sample is the group of elements collected from the population and has similar characteristics to the population.

A population parameter is the calculated value that is calculated from the population. To estimate the population parameter, one can collect a sample, and the value calculated/measured from the sample is known as a statistic.

The mean is the average of the data, which can be calculated for both mean and population data.

In this case, it is mentioned that the mean value of the scores of the students is 105.3. The mean value is obtained from the students of the specific school. If the mean value is calculated from the sample of the students, it will be considered a statistic; otherwise, it will be considered a parameter.

To find whether the given value is mean belongs to a statistic or parameter, one should ask the experimenter about the purpose of the study. The experiment should include information on whether the study is conducted to know the mean score of the specific school only or if it will be used to infer the larger population (about other schools too). Suppose the study is conducted only to infer the school's mean score. In that case, it will be considered a parameter, or if it is going to be used to infer the larger population, it will be considered a statistic.

Hence, for the information required to find whether the given mean value belongs to a statistic or parameter, one should ask the question about the use of the study. The question will be, “Are the students at this school the only ones required to be concluded, or will the study represent a bigger population?

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To evaluate the success of a 1-year experimental program designed to increase the mathematical achievement of underprivileged high school seniors, a random sample of participants in the program will be selected and their mathematics scores will be compared with the previous year’s statewide average of 525 for underprivileged seniors. The researchers want to determine whether the experimental program has increased the mean achievement level over the previous year’s statewide average. If alpha=.05, what sample size is needed to have a probability of Type II error of at most .025 if the actual mean is increased to 550? From previous results, sigma=80.

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 11, Problem 11.1E

To determine

To explain: The information that is needed to find whether the given mean value belongs to a statistic or parameter.

Expert Solution & Answer

Explanation of Solution

Given information:

The mean score of 105.3 for the students of a specific school.

Concept used:

The whole collection or group of all the elements is known as the population. The sample is the group of elements collected from the population and has similar characteristics to the population.

A population parameter is the calculated value that is calculated from the population. To estimate the population parameter, one can collect a sample, and the value calculated/measured from the sample is known as a statistic.

The mean is the average of the data, which can be calculated for both mean and population data.

In this case, it is mentioned that the mean value of the scores of the students is 105.3. The mean value is obtained from the students of the specific school. If the mean value is calculated from the sample of the students, it will be considered a statistic; otherwise, it will be considered a parameter.

To find whether the given value is mean belongs to a statistic or parameter, one should ask the experimenter about the purpose of the study. The experiment should include information on whether the study is conducted to know the mean score of the specific school only or if it will be used to infer the larger population (about other schools too). Suppose the study is conducted only to infer the school's mean score. In that case, it will be considered a parameter, or if it is going to be used to infer the larger population, it will be considered a statistic.

Hence, for the information required to find whether the given mean value belongs to a statistic or parameter, one should ask the question about the use of the study. The question will be, “Are the students at this school the only ones required to be concluded, or will the study represent a bigger population?

Want to see more full solutions like this?

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

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 11, Problem 11.1E

To determine

To explain: The information that is needed to find whether the given mean value belongs to a statistic or parameter.

Expert Solution & Answer

Explanation of Solution

Given information:

The mean score of 105.3 for the students of a specific school.

Concept used:

The whole collection or group of all the elements is known as the population. The sample is the group of elements collected from the population and has similar characteristics to the population.

A population parameter is the calculated value that is calculated from the population. To estimate the population parameter, one can collect a sample, and the value calculated/measured from the sample is known as a statistic.

The mean is the average of the data, which can be calculated for both mean and population data.

In this case, it is mentioned that the mean value of the scores of the students is 105.3. The mean value is obtained from the students of the specific school. If the mean value is calculated from the sample of the students, it will be considered a statistic; otherwise, it will be considered a parameter.

To find whether the given value is mean belongs to a statistic or parameter, one should ask the experimenter about the purpose of the study. The experiment should include information on whether the study is conducted to know the mean score of the specific school only or if it will be used to infer the larger population (about other schools too). Suppose the study is conducted only to infer the school's mean score. In that case, it will be considered a parameter, or if it is going to be used to infer the larger population, it will be considered a statistic.

Hence, for the information required to find whether the given mean value belongs to a statistic or parameter, one should ask the question about the use of the study. The question will be, “Are the students at this school the only ones required to be concluded, or will the study represent a bigger population?

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

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 11, Problem 11.1E

To determine

To explain: The information that is needed to find whether the given mean value belongs to a statistic or parameter.

Expert Solution & Answer

Explanation of Solution

Given information:

The mean score of 105.3 for the students of a specific school.

Concept used:

The whole collection or group of all the elements is known as the population. The sample is the group of elements collected from the population and has similar characteristics to the population.

A population parameter is the calculated value that is calculated from the population. To estimate the population parameter, one can collect a sample, and the value calculated/measured from the sample is known as a statistic.

The mean is the average of the data, which can be calculated for both mean and population data.

In this case, it is mentioned that the mean value of the scores of the students is 105.3. The mean value is obtained from the students of the specific school. If the mean value is calculated from the sample of the students, it will be considered a statistic; otherwise, it will be considered a parameter.

To find whether the given value is mean belongs to a statistic or parameter, one should ask the experimenter about the purpose of the study. The experiment should include information on whether the study is conducted to know the mean score of the specific school only or if it will be used to infer the larger population (about other schools too). Suppose the study is conducted only to infer the school's mean score. In that case, it will be considered a parameter, or if it is going to be used to infer the larger population, it will be considered a statistic.

Hence, for the information required to find whether the given mean value belongs to a statistic or parameter, one should ask the question about the use of the study. The question will be, “Are the students at this school the only ones required to be concluded, or will the study represent a bigger population?

Want to see more full solutions like this?

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

Answer 5

Chapter 11, Problem 11.1E

To determine

To explain: The information that is needed to find whether the given mean value belongs to a statistic or parameter.

Expert Solution & Answer

Explanation of Solution

Given information:

The mean score of 105.3 for the students of a specific school.

Concept used:

The whole collection or group of all the elements is known as the population. The sample is the group of elements collected from the population and has similar characteristics to the population.

A population parameter is the calculated value that is calculated from the population. To estimate the population parameter, one can collect a sample, and the value calculated/measured from the sample is known as a statistic.

The mean is the average of the data, which can be calculated for both mean and population data.

In this case, it is mentioned that the mean value of the scores of the students is 105.3. The mean value is obtained from the students of the specific school. If the mean value is calculated from the sample of the students, it will be considered a statistic; otherwise, it will be considered a parameter.

To find whether the given value is mean belongs to a statistic or parameter, one should ask the experimenter about the purpose of the study. The experiment should include information on whether the study is conducted to know the mean score of the specific school only or if it will be used to infer the larger population (about other schools too). Suppose the study is conducted only to infer the school's mean score. In that case, it will be considered a parameter, or if it is going to be used to infer the larger population, it will be considered a statistic.

Hence, for the information required to find whether the given mean value belongs to a statistic or parameter, one should ask the question about the use of the study. The question will be, “Are the students at this school the only ones required to be concluded, or will the study represent a bigger population?

Answer 6

Chapter 11, Problem 11.1E

To determine

To explain: The information that is needed to find whether the given mean value belongs to a statistic or parameter.

Expert Solution & Answer

Explanation of Solution

Given information:

The mean score of 105.3 for the students of a specific school.

Concept used:

The whole collection or group of all the elements is known as the population. The sample is the group of elements collected from the population and has similar characteristics to the population.

A population parameter is the calculated value that is calculated from the population. To estimate the population parameter, one can collect a sample, and the value calculated/measured from the sample is known as a statistic.

The mean is the average of the data, which can be calculated for both mean and population data.

In this case, it is mentioned that the mean value of the scores of the students is 105.3. The mean value is obtained from the students of the specific school. If the mean value is calculated from the sample of the students, it will be considered a statistic; otherwise, it will be considered a parameter.

To find whether the given value is mean belongs to a statistic or parameter, one should ask the experimenter about the purpose of the study. The experiment should include information on whether the study is conducted to know the mean score of the specific school only or if it will be used to infer the larger population (about other schools too). Suppose the study is conducted only to infer the school's mean score. In that case, it will be considered a parameter, or if it is going to be used to infer the larger population, it will be considered a statistic.

Hence, for the information required to find whether the given mean value belongs to a statistic or parameter, one should ask the question about the use of the study. The question will be, “Are the students at this school the only ones required to be concluded, or will the study represent a bigger population?

Answer 7

Chapter 11, Problem 11.1E

To determine

To explain: The information that is needed to find whether the given mean value belongs to a statistic or parameter.

Answer 8

Expert Solution & Answer

Explanation of Solution

Given information:

The mean score of 105.3 for the students of a specific school.

Concept used:

The whole collection or group of all the elements is known as the population. The sample is the group of elements collected from the population and has similar characteristics to the population.

A population parameter is the calculated value that is calculated from the population. To estimate the population parameter, one can collect a sample, and the value calculated/measured from the sample is known as a statistic.

The mean is the average of the data, which can be calculated for both mean and population data.

In this case, it is mentioned that the mean value of the scores of the students is 105.3. The mean value is obtained from the students of the specific school. If the mean value is calculated from the sample of the students, it will be considered a statistic; otherwise, it will be considered a parameter.

To find whether the given value is mean belongs to a statistic or parameter, one should ask the experimenter about the purpose of the study. The experiment should include information on whether the study is conducted to know the mean score of the specific school only or if it will be used to infer the larger population (about other schools too). Suppose the study is conducted only to infer the school's mean score. In that case, it will be considered a parameter, or if it is going to be used to infer the larger population, it will be considered a statistic.

Hence, for the information required to find whether the given mean value belongs to a statistic or parameter, one should ask the question about the use of the study. The question will be, “Are the students at this school the only ones required to be concluded, or will the study represent a bigger population?