The annual incomes of a sample of middle-management employees at Westinghouse are $62,900, $69,100, $58,300, and $76,800. (a) Give the formula for the sample mean . (b) Find the sample mean. (c) Is the mean you computed in (b) a statistic or a parameter? Why? (d) What is your best estimate of the population mean?

Question

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Answer 1

Textbook Question

Chapter 3, Problem 1.1SR

The annual incomes of a sample of middle-management employees at Westinghouse are $62,900, $69,100, $58,300, and $76,800.

(a) Give the formula for the sample mean.
(b) Find the sample mean.
(c) Is the mean you computed in (b) a statistic or a parameter? Why?
(d) What is your best estimate of the population mean?

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

Mention the formula for the sample mean.

Answer to Problem 1.1SR

The formula for sample mean is x¯=∑xn.

Explanation of Solution

Sample mean:

The sample mean is the sum of all data values in the sample, divided by total number of data values from the sample. The formula for sample mean is,

Sample mean=Sum of all the values in the sampleNumber of values in the sample

In notations the formula for sample mean is,

x¯=∑xn

In the formula, x¯ denotes the sample mean, ∑x denotes sum of all sample values and n is the size of sample.

(b)

Expert Solution

To determine

Find the sample mean for a sample of annual incomes of middle-management employees at Westinghouse.

Answer to Problem 1.1SR

The sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

Explanation of Solution

Calculation:

The number of data values in the sample is 4.

Add all values of sample for ‘∑x’ and substitute 4 for ‘n’ in sample mean formula.

x¯=$62,900+$69,100+$58,300+$76,8004=$267,1004=$66,775

Hence, the sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

(c)

Expert Solution

To determine

Identify whether the mean is a statistic or parameter.

Answer to Problem 1.1SR

The mean calculated is a statistic as it is calculated for the sample values.

Explanation of Solution

Parameter:

The characteristic that is measurable for a population in the study is denoted as parameter.

Statistic:

The characteristic that is measurable for a sample in the study is denoted as statistic.

The mean is calculated for a sample of annual incomes middle-management employees at Westinghouse. Since mean is calculated for the sample data values it would represent the measurable characteristic for the sample. This shows that, the mean calculated is a statistic.

Hence, the mean calculated is a statistic as it is calculated for the sample values.

(d)

Expert Solution

To determine

Find the best estimate of the population mean.

Answer to Problem 1.1SR

The best estimate of the population mean is sample mean value $66,775.

Explanation of Solution

The best estimate for any population is its sample. Thus, the best estimate for the population mean would be its sample mean.

The sample mean for annual incomes of middle-management employees at Westinghouse is $66,775. The value $66,775 would be the best estimate for population mean.

Hence, the best estimate of the population mean is sample mean value $66,775.

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Answer 2

Textbook Question

Chapter 3, Problem 1.1SR

The annual incomes of a sample of middle-management employees at Westinghouse are $62,900, $69,100, $58,300, and $76,800.

(a) Give the formula for the sample mean.
(b) Find the sample mean.
(c) Is the mean you computed in (b) a statistic or a parameter? Why?
(d) What is your best estimate of the population mean?

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

Mention the formula for the sample mean.

Answer to Problem 1.1SR

The formula for sample mean is x¯=∑xn.

Explanation of Solution

Sample mean:

The sample mean is the sum of all data values in the sample, divided by total number of data values from the sample. The formula for sample mean is,

Sample mean=Sum of all the values in the sampleNumber of values in the sample

In notations the formula for sample mean is,

x¯=∑xn

In the formula, x¯ denotes the sample mean, ∑x denotes sum of all sample values and n is the size of sample.

(b)

Expert Solution

To determine

Find the sample mean for a sample of annual incomes of middle-management employees at Westinghouse.

Answer to Problem 1.1SR

The sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

Explanation of Solution

Calculation:

The number of data values in the sample is 4.

Add all values of sample for ‘∑x’ and substitute 4 for ‘n’ in sample mean formula.

x¯=$62,900+$69,100+$58,300+$76,8004=$267,1004=$66,775

Hence, the sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

(c)

Expert Solution

To determine

Identify whether the mean is a statistic or parameter.

Answer to Problem 1.1SR

The mean calculated is a statistic as it is calculated for the sample values.

Explanation of Solution

Parameter:

The characteristic that is measurable for a population in the study is denoted as parameter.

Statistic:

The characteristic that is measurable for a sample in the study is denoted as statistic.

The mean is calculated for a sample of annual incomes middle-management employees at Westinghouse. Since mean is calculated for the sample data values it would represent the measurable characteristic for the sample. This shows that, the mean calculated is a statistic.

Hence, the mean calculated is a statistic as it is calculated for the sample values.

(d)

Expert Solution

To determine

Find the best estimate of the population mean.

Answer to Problem 1.1SR

The best estimate of the population mean is sample mean value $66,775.

Explanation of Solution

The best estimate for any population is its sample. Thus, the best estimate for the population mean would be its sample mean.

The sample mean for annual incomes of middle-management employees at Westinghouse is $66,775. The value $66,775 would be the best estimate for population mean.

Hence, the best estimate of the population mean is sample mean value $66,775.

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Answer 3

Textbook Question

Chapter 3, Problem 1.1SR

The annual incomes of a sample of middle-management employees at Westinghouse are $62,900, $69,100, $58,300, and $76,800.

(a) Give the formula for the sample mean.
(b) Find the sample mean.
(c) Is the mean you computed in (b) a statistic or a parameter? Why?
(d) What is your best estimate of the population mean?

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

Mention the formula for the sample mean.

Answer to Problem 1.1SR

The formula for sample mean is x¯=∑xn.

Explanation of Solution

Sample mean:

The sample mean is the sum of all data values in the sample, divided by total number of data values from the sample. The formula for sample mean is,

Sample mean=Sum of all the values in the sampleNumber of values in the sample

In notations the formula for sample mean is,

x¯=∑xn

In the formula, x¯ denotes the sample mean, ∑x denotes sum of all sample values and n is the size of sample.

(b)

Expert Solution

To determine

Find the sample mean for a sample of annual incomes of middle-management employees at Westinghouse.

Answer to Problem 1.1SR

The sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

Explanation of Solution

Calculation:

The number of data values in the sample is 4.

Add all values of sample for ‘∑x’ and substitute 4 for ‘n’ in sample mean formula.

x¯=$62,900+$69,100+$58,300+$76,8004=$267,1004=$66,775

Hence, the sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

(c)

Expert Solution

To determine

Identify whether the mean is a statistic or parameter.

Answer to Problem 1.1SR

The mean calculated is a statistic as it is calculated for the sample values.

Explanation of Solution

Parameter:

The characteristic that is measurable for a population in the study is denoted as parameter.

Statistic:

The characteristic that is measurable for a sample in the study is denoted as statistic.

The mean is calculated for a sample of annual incomes middle-management employees at Westinghouse. Since mean is calculated for the sample data values it would represent the measurable characteristic for the sample. This shows that, the mean calculated is a statistic.

Hence, the mean calculated is a statistic as it is calculated for the sample values.

(d)

Expert Solution

To determine

Find the best estimate of the population mean.

Answer to Problem 1.1SR

The best estimate of the population mean is sample mean value $66,775.

Explanation of Solution

The best estimate for any population is its sample. Thus, the best estimate for the population mean would be its sample mean.

The sample mean for annual incomes of middle-management employees at Westinghouse is $66,775. The value $66,775 would be the best estimate for population mean.

Hence, the best estimate of the population mean is sample mean value $66,775.

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Answer 4

Textbook Question

Chapter 3, Problem 1.1SR

The annual incomes of a sample of middle-management employees at Westinghouse are $62,900, $69,100, $58,300, and $76,800.

(a) Give the formula for the sample mean.
(b) Find the sample mean.
(c) Is the mean you computed in (b) a statistic or a parameter? Why?
(d) What is your best estimate of the population mean?

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

Mention the formula for the sample mean.

Answer to Problem 1.1SR

The formula for sample mean is x¯=∑xn.

Explanation of Solution

Sample mean:

The sample mean is the sum of all data values in the sample, divided by total number of data values from the sample. The formula for sample mean is,

Sample mean=Sum of all the values in the sampleNumber of values in the sample

In notations the formula for sample mean is,

x¯=∑xn

In the formula, x¯ denotes the sample mean, ∑x denotes sum of all sample values and n is the size of sample.

(b)

Expert Solution

To determine

Find the sample mean for a sample of annual incomes of middle-management employees at Westinghouse.

Answer to Problem 1.1SR

The sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

Explanation of Solution

Calculation:

The number of data values in the sample is 4.

Add all values of sample for ‘∑x’ and substitute 4 for ‘n’ in sample mean formula.

x¯=$62,900+$69,100+$58,300+$76,8004=$267,1004=$66,775

Hence, the sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

(c)

Expert Solution

To determine

Identify whether the mean is a statistic or parameter.

Answer to Problem 1.1SR

The mean calculated is a statistic as it is calculated for the sample values.

Explanation of Solution

Parameter:

The characteristic that is measurable for a population in the study is denoted as parameter.

Statistic:

The characteristic that is measurable for a sample in the study is denoted as statistic.

The mean is calculated for a sample of annual incomes middle-management employees at Westinghouse. Since mean is calculated for the sample data values it would represent the measurable characteristic for the sample. This shows that, the mean calculated is a statistic.

Hence, the mean calculated is a statistic as it is calculated for the sample values.

(d)

Expert Solution

To determine

Find the best estimate of the population mean.

Answer to Problem 1.1SR

The best estimate of the population mean is sample mean value $66,775.

Explanation of Solution

The best estimate for any population is its sample. Thus, the best estimate for the population mean would be its sample mean.

The sample mean for annual incomes of middle-management employees at Westinghouse is $66,775. The value $66,775 would be the best estimate for population mean.

Hence, the best estimate of the population mean is sample mean value $66,775.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

Mention the formula for the sample mean.

Answer to Problem 1.1SR

The formula for sample mean is x¯=∑xn.

Explanation of Solution

Sample mean:

The sample mean is the sum of all data values in the sample, divided by total number of data values from the sample. The formula for sample mean is,

Sample mean=Sum of all the values in the sampleNumber of values in the sample

In notations the formula for sample mean is,

x¯=∑xn

In the formula, x¯ denotes the sample mean, ∑x denotes sum of all sample values and n is the size of sample.

(b)

Expert Solution

To determine

Find the sample mean for a sample of annual incomes of middle-management employees at Westinghouse.

Answer to Problem 1.1SR

The sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

Explanation of Solution

Calculation:

The number of data values in the sample is 4.

Add all values of sample for ‘∑x’ and substitute 4 for ‘n’ in sample mean formula.

x¯=$62,900+$69,100+$58,300+$76,8004=$267,1004=$66,775

Hence, the sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

(c)

Expert Solution

To determine

Identify whether the mean is a statistic or parameter.

Answer to Problem 1.1SR

The mean calculated is a statistic as it is calculated for the sample values.

Explanation of Solution

Parameter:

The characteristic that is measurable for a population in the study is denoted as parameter.

Statistic:

The characteristic that is measurable for a sample in the study is denoted as statistic.

The mean is calculated for a sample of annual incomes middle-management employees at Westinghouse. Since mean is calculated for the sample data values it would represent the measurable characteristic for the sample. This shows that, the mean calculated is a statistic.

Hence, the mean calculated is a statistic as it is calculated for the sample values.

(d)

Expert Solution

To determine

Find the best estimate of the population mean.

Answer to Problem 1.1SR

The best estimate of the population mean is sample mean value $66,775.

Explanation of Solution

The best estimate for any population is its sample. Thus, the best estimate for the population mean would be its sample mean.

The sample mean for annual incomes of middle-management employees at Westinghouse is $66,775. The value $66,775 would be the best estimate for population mean.

Hence, the best estimate of the population mean is sample mean value $66,775.

Answer 8

(a)

Expert Solution

To determine

Mention the formula for the sample mean.

Answer to Problem 1.1SR

The formula for sample mean is x¯=∑xn.

Explanation of Solution

Sample mean:

The sample mean is the sum of all data values in the sample, divided by total number of data values from the sample. The formula for sample mean is,

Sample mean=Sum of all the values in the sampleNumber of values in the sample

In notations the formula for sample mean is,

x¯=∑xn

In the formula, x¯ denotes the sample mean, ∑x denotes sum of all sample values and n is the size of sample.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Mention the formula for the sample mean.

Answer 13

Answer to Problem 1.1SR

The formula for sample mean is x¯=∑xn.

Answer 14

Explanation of Solution

Sample mean:

The sample mean is the sum of all data values in the sample, divided by total number of data values from the sample. The formula for sample mean is,

Sample mean=Sum of all the values in the sampleNumber of values in the sample

In notations the formula for sample mean is,

x¯=∑xn

In the formula, x¯ denotes the sample mean, ∑x denotes sum of all sample values and n is the size of sample.

Answer 15

(b)

Expert Solution

To determine

Find the sample mean for a sample of annual incomes of middle-management employees at Westinghouse.

Answer to Problem 1.1SR

The sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

Explanation of Solution

Calculation:

The number of data values in the sample is 4.

Add all values of sample for ‘∑x’ and substitute 4 for ‘n’ in sample mean formula.

x¯=$62,900+$69,100+$58,300+$76,8004=$267,1004=$66,775

Hence, the sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Find the sample mean for a sample of annual incomes of middle-management employees at Westinghouse.

Answer 20

Answer to Problem 1.1SR

The sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

Answer 21

Explanation of Solution

Calculation:

The number of data values in the sample is 4.

Add all values of sample for ‘∑x’ and substitute 4 for ‘n’ in sample mean formula.

x¯=$62,900+$69,100+$58,300+$76,8004=$267,1004=$66,775

Hence, the sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.

Answer 22

(c)

Expert Solution

To determine

Identify whether the mean is a statistic or parameter.

Answer to Problem 1.1SR

The mean calculated is a statistic as it is calculated for the sample values.

Explanation of Solution

Parameter:

The characteristic that is measurable for a population in the study is denoted as parameter.

Statistic:

The characteristic that is measurable for a sample in the study is denoted as statistic.

The mean is calculated for a sample of annual incomes middle-management employees at Westinghouse. Since mean is calculated for the sample data values it would represent the measurable characteristic for the sample. This shows that, the mean calculated is a statistic.

Hence, the mean calculated is a statistic as it is calculated for the sample values.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

Identify whether the mean is a statistic or parameter.

Answer 27

Answer to Problem 1.1SR

The mean calculated is a statistic as it is calculated for the sample values.

Answer 28

Explanation of Solution

Parameter:

The characteristic that is measurable for a population in the study is denoted as parameter.

Statistic:

The characteristic that is measurable for a sample in the study is denoted as statistic.

The mean is calculated for a sample of annual incomes middle-management employees at Westinghouse. Since mean is calculated for the sample data values it would represent the measurable characteristic for the sample. This shows that, the mean calculated is a statistic.

Hence, the mean calculated is a statistic as it is calculated for the sample values.

Answer 29

(d)

Expert Solution

To determine

Find the best estimate of the population mean.

Answer to Problem 1.1SR

The best estimate of the population mean is sample mean value $66,775.

Explanation of Solution

The best estimate for any population is its sample. Thus, the best estimate for the population mean would be its sample mean.

The sample mean for annual incomes of middle-management employees at Westinghouse is $66,775. The value $66,775 would be the best estimate for population mean.

Hence, the best estimate of the population mean is sample mean value $66,775.

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

Find the best estimate of the population mean.

Answer 34

Answer to Problem 1.1SR

The best estimate of the population mean is sample mean value $66,775.

Answer 35

Explanation of Solution

The best estimate for any population is its sample. Thus, the best estimate for the population mean would be its sample mean.

The sample mean for annual incomes of middle-management employees at Westinghouse is $66,775. The value $66,775 would be the best estimate for population mean.

Hence, the best estimate of the population mean is sample mean value $66,775.