The population mean of 10 players.

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 5.2, Problem 27E

(a)

To determine

The population mean of 10 players.

(a)

Expert Solution

Answer to Problem 27E

Solution: The population mean is 120.5_.

Explanation of Solution

The population mean is calculated as given below.

PlayerTotal time(X)098163213732104525886151713381059168∑i=09Xi=1205

μ=∑i=1nXin=120510=120.5

Hence, the population mean is 120.5.

(b)

To determine

The simple random sample of size 3.

(b)

Expert Solution

Answer to Problem 27E

Solution: The selected simple random sample is the players numbered 1, 9, and 2.

Explanation of Solution

There are nine players numbered 0,1…9. The players in this study are selected using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column. The random number is selected between 0 and 9. The obtained samples are 1, 9, and 2. The players who have the same numbers with the selected random numbers will be included in the sample.

To determine

The sample mean.

Expert Solution

Answer to Problem 27E

Solution: The sample mean is 122.67_.

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=63+168+1373=3683=122.67

The sample mean of sample observations 1, 9, and 2 is 122.67.

(c)

To determine

The simple random samples of size 3 nine times.

(c)

Expert Solution

Answer to Problem 27E

Solution: The simple random samples obtained are

(9,5,0),(0,5,7),(2,8,7),(9,6,4),(1,2,5),(4,2,5),(8,2,8),(7,3,6),(4,7,1)_

Explanation of Solution

There are nine players numbered 0,1,..,9. The players in this study are chosen using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column of the table. The random number is selected between 0 and 9. The obtained samples are 9, 5, and 0. The players who have the same numbers with the selected random numbers are included in the sample. The remaining eight samples are drawn in the similar manner.

Hence, the table of all the 10 samples obtained is drawn as

Sample numberSample observations1(1,9,2)2(9,5,0)3(0,5,7)4(2,8,7)5(9,6,4)6(1,2,5)7(4,2,5)8(8,2,8)9(7,3,6)10(4,7,1)

To determine

The sample mean of the simple random samples drawn above.

Expert Solution

Answer to Problem 27E

Solution: The sample mean for each simple random sample is shown in the table below.

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=168+88+983=118

The sample means for 10 random samples are computed in a similar way. The table showing calculation for the computation of the sample mean is drawn below:

Sample numberSimple random samples Sample ObservationsSample mean11,9,263,168,13763+168+1373=122.6729,5,0168,88,98168+88+983=11830,5,798,88,13398+88+1333=106.3342,8,7137,105,133137+105+1333=12559,6,4168,151,52168+151+523=123.6761,2,563,137,8863+137+883=9674,2,552,137,5552+137+553=81.3388,2,8105,137,105105+137+1053=115.6797,3,6133,210,151133+210+1513=164.67104,7,152,133,6352+133+633=82.67

To determine

To graph: The histogram showing the 10 values of sample mean.

Expert Solution

Explanation of Solution

The histogram showing the values of 10 sample mean is drawn in Minitab. The steps are written below:

Step 1. Enter the data in Minitab classifying the sample mean of 10 samples.

Step 2. Click on Graph in toolbox and click on histogram.

Step 3. Next, choose simple histogram option appearing in the dialog box and click OK.

Step 4. Drag the sample mean appearing on the left side in Graph variables and click on OK..

Graph: The obtained histogram showing the frequency and sample mean is as follows:

Introduction to the Practice of Statistics, Chapter 5.2, Problem 27E

(d)

To determine

Whether the center of the histogram is close to population mean.

(d)

Expert Solution

Answer to Problem 27E

Solution: The center of the histogram is close to population mean.

Explanation of Solution

The histogram drawn in part (c) shows that the sample means of 10 samples are close to 120 and the population mean computed in part (a) is equal to 120.5. This shows that the population mean is approximately equal to the sample means obtained by drawing 10 simple random samples from the population.

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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 5.2, Problem 27E

(a)

To determine

The population mean of 10 players.

(a)

Expert Solution

Answer to Problem 27E

Solution: The population mean is 120.5_.

Explanation of Solution

The population mean is calculated as given below.

PlayerTotal time(X)098163213732104525886151713381059168∑i=09Xi=1205

μ=∑i=1nXin=120510=120.5

Hence, the population mean is 120.5.

(b)

To determine

The simple random sample of size 3.

(b)

Expert Solution

Answer to Problem 27E

Solution: The selected simple random sample is the players numbered 1, 9, and 2.

Explanation of Solution

There are nine players numbered 0,1…9. The players in this study are selected using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column. The random number is selected between 0 and 9. The obtained samples are 1, 9, and 2. The players who have the same numbers with the selected random numbers will be included in the sample.

To determine

The sample mean.

Expert Solution

Answer to Problem 27E

Solution: The sample mean is 122.67_.

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=63+168+1373=3683=122.67

The sample mean of sample observations 1, 9, and 2 is 122.67.

(c)

To determine

The simple random samples of size 3 nine times.

(c)

Expert Solution

Answer to Problem 27E

Solution: The simple random samples obtained are

(9,5,0),(0,5,7),(2,8,7),(9,6,4),(1,2,5),(4,2,5),(8,2,8),(7,3,6),(4,7,1)_

Explanation of Solution

There are nine players numbered 0,1,..,9. The players in this study are chosen using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column of the table. The random number is selected between 0 and 9. The obtained samples are 9, 5, and 0. The players who have the same numbers with the selected random numbers are included in the sample. The remaining eight samples are drawn in the similar manner.

Hence, the table of all the 10 samples obtained is drawn as

Sample numberSample observations1(1,9,2)2(9,5,0)3(0,5,7)4(2,8,7)5(9,6,4)6(1,2,5)7(4,2,5)8(8,2,8)9(7,3,6)10(4,7,1)

To determine

The sample mean of the simple random samples drawn above.

Expert Solution

Answer to Problem 27E

Solution: The sample mean for each simple random sample is shown in the table below.

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=168+88+983=118

The sample means for 10 random samples are computed in a similar way. The table showing calculation for the computation of the sample mean is drawn below:

Sample numberSimple random samples Sample ObservationsSample mean11,9,263,168,13763+168+1373=122.6729,5,0168,88,98168+88+983=11830,5,798,88,13398+88+1333=106.3342,8,7137,105,133137+105+1333=12559,6,4168,151,52168+151+523=123.6761,2,563,137,8863+137+883=9674,2,552,137,5552+137+553=81.3388,2,8105,137,105105+137+1053=115.6797,3,6133,210,151133+210+1513=164.67104,7,152,133,6352+133+633=82.67

To determine

To graph: The histogram showing the 10 values of sample mean.

Expert Solution

Explanation of Solution

The histogram showing the values of 10 sample mean is drawn in Minitab. The steps are written below:

Step 1. Enter the data in Minitab classifying the sample mean of 10 samples.

Step 2. Click on Graph in toolbox and click on histogram.

Step 3. Next, choose simple histogram option appearing in the dialog box and click OK.

Step 4. Drag the sample mean appearing on the left side in Graph variables and click on OK..

Graph: The obtained histogram showing the frequency and sample mean is as follows:

Introduction to the Practice of Statistics, Chapter 5.2, Problem 27E

(d)

To determine

Whether the center of the histogram is close to population mean.

(d)

Expert Solution

Answer to Problem 27E

Solution: The center of the histogram is close to population mean.

Explanation of Solution

The histogram drawn in part (c) shows that the sample means of 10 samples are close to 120 and the population mean computed in part (a) is equal to 120.5. This shows that the population mean is approximately equal to the sample means obtained by drawing 10 simple random samples from the population.

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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 5.2, Problem 27E

(a)

To determine

The population mean of 10 players.

(a)

Expert Solution

Answer to Problem 27E

Solution: The population mean is 120.5_.

Explanation of Solution

The population mean is calculated as given below.

PlayerTotal time(X)098163213732104525886151713381059168∑i=09Xi=1205

μ=∑i=1nXin=120510=120.5

Hence, the population mean is 120.5.

(b)

To determine

The simple random sample of size 3.

(b)

Expert Solution

Answer to Problem 27E

Solution: The selected simple random sample is the players numbered 1, 9, and 2.

Explanation of Solution

There are nine players numbered 0,1…9. The players in this study are selected using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column. The random number is selected between 0 and 9. The obtained samples are 1, 9, and 2. The players who have the same numbers with the selected random numbers will be included in the sample.

To determine

The sample mean.

Expert Solution

Answer to Problem 27E

Solution: The sample mean is 122.67_.

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=63+168+1373=3683=122.67

The sample mean of sample observations 1, 9, and 2 is 122.67.

(c)

To determine

The simple random samples of size 3 nine times.

(c)

Expert Solution

Answer to Problem 27E

Solution: The simple random samples obtained are

(9,5,0),(0,5,7),(2,8,7),(9,6,4),(1,2,5),(4,2,5),(8,2,8),(7,3,6),(4,7,1)_

Explanation of Solution

There are nine players numbered 0,1,..,9. The players in this study are chosen using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column of the table. The random number is selected between 0 and 9. The obtained samples are 9, 5, and 0. The players who have the same numbers with the selected random numbers are included in the sample. The remaining eight samples are drawn in the similar manner.

Hence, the table of all the 10 samples obtained is drawn as

Sample numberSample observations1(1,9,2)2(9,5,0)3(0,5,7)4(2,8,7)5(9,6,4)6(1,2,5)7(4,2,5)8(8,2,8)9(7,3,6)10(4,7,1)

To determine

The sample mean of the simple random samples drawn above.

Expert Solution

Answer to Problem 27E

Solution: The sample mean for each simple random sample is shown in the table below.

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=168+88+983=118

The sample means for 10 random samples are computed in a similar way. The table showing calculation for the computation of the sample mean is drawn below:

Sample numberSimple random samples Sample ObservationsSample mean11,9,263,168,13763+168+1373=122.6729,5,0168,88,98168+88+983=11830,5,798,88,13398+88+1333=106.3342,8,7137,105,133137+105+1333=12559,6,4168,151,52168+151+523=123.6761,2,563,137,8863+137+883=9674,2,552,137,5552+137+553=81.3388,2,8105,137,105105+137+1053=115.6797,3,6133,210,151133+210+1513=164.67104,7,152,133,6352+133+633=82.67

To determine

To graph: The histogram showing the 10 values of sample mean.

Expert Solution

Explanation of Solution

The histogram showing the values of 10 sample mean is drawn in Minitab. The steps are written below:

Step 1. Enter the data in Minitab classifying the sample mean of 10 samples.

Step 2. Click on Graph in toolbox and click on histogram.

Step 3. Next, choose simple histogram option appearing in the dialog box and click OK.

Step 4. Drag the sample mean appearing on the left side in Graph variables and click on OK..

Graph: The obtained histogram showing the frequency and sample mean is as follows:

Introduction to the Practice of Statistics, Chapter 5.2, Problem 27E

(d)

To determine

Whether the center of the histogram is close to population mean.

(d)

Expert Solution

Answer to Problem 27E

Solution: The center of the histogram is close to population mean.

Explanation of Solution

The histogram drawn in part (c) shows that the sample means of 10 samples are close to 120 and the population mean computed in part (a) is equal to 120.5. This shows that the population mean is approximately equal to the sample means obtained by drawing 10 simple random samples from the population.

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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 5.2, Problem 27E

(a)

To determine

The population mean of 10 players.

(a)

Expert Solution

Answer to Problem 27E

Solution: The population mean is 120.5_.

Explanation of Solution

The population mean is calculated as given below.

PlayerTotal time(X)098163213732104525886151713381059168∑i=09Xi=1205

μ=∑i=1nXin=120510=120.5

Hence, the population mean is 120.5.

(b)

To determine

The simple random sample of size 3.

(b)

Expert Solution

Answer to Problem 27E

Solution: The selected simple random sample is the players numbered 1, 9, and 2.

Explanation of Solution

There are nine players numbered 0,1…9. The players in this study are selected using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column. The random number is selected between 0 and 9. The obtained samples are 1, 9, and 2. The players who have the same numbers with the selected random numbers will be included in the sample.

To determine

The sample mean.

Expert Solution

Answer to Problem 27E

Solution: The sample mean is 122.67_.

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=63+168+1373=3683=122.67

The sample mean of sample observations 1, 9, and 2 is 122.67.

(c)

To determine

The simple random samples of size 3 nine times.

(c)

Expert Solution

Answer to Problem 27E

Solution: The simple random samples obtained are

(9,5,0),(0,5,7),(2,8,7),(9,6,4),(1,2,5),(4,2,5),(8,2,8),(7,3,6),(4,7,1)_

Explanation of Solution

There are nine players numbered 0,1,..,9. The players in this study are chosen using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column of the table. The random number is selected between 0 and 9. The obtained samples are 9, 5, and 0. The players who have the same numbers with the selected random numbers are included in the sample. The remaining eight samples are drawn in the similar manner.

Hence, the table of all the 10 samples obtained is drawn as

Sample numberSample observations1(1,9,2)2(9,5,0)3(0,5,7)4(2,8,7)5(9,6,4)6(1,2,5)7(4,2,5)8(8,2,8)9(7,3,6)10(4,7,1)

To determine

The sample mean of the simple random samples drawn above.

Expert Solution

Answer to Problem 27E

Solution: The sample mean for each simple random sample is shown in the table below.

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=168+88+983=118

The sample means for 10 random samples are computed in a similar way. The table showing calculation for the computation of the sample mean is drawn below:

Sample numberSimple random samples Sample ObservationsSample mean11,9,263,168,13763+168+1373=122.6729,5,0168,88,98168+88+983=11830,5,798,88,13398+88+1333=106.3342,8,7137,105,133137+105+1333=12559,6,4168,151,52168+151+523=123.6761,2,563,137,8863+137+883=9674,2,552,137,5552+137+553=81.3388,2,8105,137,105105+137+1053=115.6797,3,6133,210,151133+210+1513=164.67104,7,152,133,6352+133+633=82.67

To determine

To graph: The histogram showing the 10 values of sample mean.

Expert Solution

Explanation of Solution

The histogram showing the values of 10 sample mean is drawn in Minitab. The steps are written below:

Step 1. Enter the data in Minitab classifying the sample mean of 10 samples.

Step 2. Click on Graph in toolbox and click on histogram.

Step 3. Next, choose simple histogram option appearing in the dialog box and click OK.

Step 4. Drag the sample mean appearing on the left side in Graph variables and click on OK..

Graph: The obtained histogram showing the frequency and sample mean is as follows:

Introduction to the Practice of Statistics, Chapter 5.2, Problem 27E

(d)

To determine

Whether the center of the histogram is close to population mean.

(d)

Expert Solution

Answer to Problem 27E

Solution: The center of the histogram is close to population mean.

Explanation of Solution

The histogram drawn in part (c) shows that the sample means of 10 samples are close to 120 and the population mean computed in part (a) is equal to 120.5. This shows that the population mean is approximately equal to the sample means obtained by drawing 10 simple random samples from the population.

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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 5.2, Problem 27E

(a)

To determine

The population mean of 10 players.

(a)

Expert Solution

Answer to Problem 27E

Solution: The population mean is 120.5_.

Explanation of Solution

The population mean is calculated as given below.

PlayerTotal time(X)098163213732104525886151713381059168∑i=09Xi=1205

μ=∑i=1nXin=120510=120.5

Hence, the population mean is 120.5.

(b)

To determine

The simple random sample of size 3.

(b)

Expert Solution

Answer to Problem 27E

Solution: The selected simple random sample is the players numbered 1, 9, and 2.

Explanation of Solution

There are nine players numbered 0,1…9. The players in this study are selected using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column. The random number is selected between 0 and 9. The obtained samples are 1, 9, and 2. The players who have the same numbers with the selected random numbers will be included in the sample.

To determine

The sample mean.

Expert Solution

Answer to Problem 27E

Solution: The sample mean is 122.67_.

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=63+168+1373=3683=122.67

The sample mean of sample observations 1, 9, and 2 is 122.67.

(c)

To determine

The simple random samples of size 3 nine times.

(c)

Expert Solution

Answer to Problem 27E

Solution: The simple random samples obtained are

(9,5,0),(0,5,7),(2,8,7),(9,6,4),(1,2,5),(4,2,5),(8,2,8),(7,3,6),(4,7,1)_

Explanation of Solution

There are nine players numbered 0,1,..,9. The players in this study are chosen using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column of the table. The random number is selected between 0 and 9. The obtained samples are 9, 5, and 0. The players who have the same numbers with the selected random numbers are included in the sample. The remaining eight samples are drawn in the similar manner.

Hence, the table of all the 10 samples obtained is drawn as

Sample numberSample observations1(1,9,2)2(9,5,0)3(0,5,7)4(2,8,7)5(9,6,4)6(1,2,5)7(4,2,5)8(8,2,8)9(7,3,6)10(4,7,1)

To determine

The sample mean of the simple random samples drawn above.

Expert Solution

Answer to Problem 27E

Solution: The sample mean for each simple random sample is shown in the table below.

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=168+88+983=118

The sample means for 10 random samples are computed in a similar way. The table showing calculation for the computation of the sample mean is drawn below:

Sample numberSimple random samples Sample ObservationsSample mean11,9,263,168,13763+168+1373=122.6729,5,0168,88,98168+88+983=11830,5,798,88,13398+88+1333=106.3342,8,7137,105,133137+105+1333=12559,6,4168,151,52168+151+523=123.6761,2,563,137,8863+137+883=9674,2,552,137,5552+137+553=81.3388,2,8105,137,105105+137+1053=115.6797,3,6133,210,151133+210+1513=164.67104,7,152,133,6352+133+633=82.67

To determine

To graph: The histogram showing the 10 values of sample mean.

Expert Solution

Explanation of Solution

The histogram showing the values of 10 sample mean is drawn in Minitab. The steps are written below:

Step 1. Enter the data in Minitab classifying the sample mean of 10 samples.

Step 2. Click on Graph in toolbox and click on histogram.

Step 3. Next, choose simple histogram option appearing in the dialog box and click OK.

Step 4. Drag the sample mean appearing on the left side in Graph variables and click on OK..

Graph: The obtained histogram showing the frequency and sample mean is as follows:

Introduction to the Practice of Statistics, Chapter 5.2, Problem 27E

(d)

To determine

Whether the center of the histogram is close to population mean.

(d)

Expert Solution

Answer to Problem 27E

Solution: The center of the histogram is close to population mean.

Explanation of Solution

The histogram drawn in part (c) shows that the sample means of 10 samples are close to 120 and the population mean computed in part (a) is equal to 120.5. This shows that the population mean is approximately equal to the sample means obtained by drawing 10 simple random samples from the population.

Answer 6

Chapter 5.2, Problem 27E

(a)

To determine

The population mean of 10 players.

(a)

Expert Solution

Answer to Problem 27E

Solution: The population mean is 120.5_.

Explanation of Solution

The population mean is calculated as given below.

PlayerTotal time(X)098163213732104525886151713381059168∑i=09Xi=1205

μ=∑i=1nXin=120510=120.5

Hence, the population mean is 120.5.

Answer 7

Chapter 5.2, Problem 27E

(a)

To determine

The population mean of 10 players.

Answer 8

(a)

Expert Solution

Answer to Problem 27E

Solution: The population mean is 120.5_.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

The population mean is calculated as given below.

PlayerTotal time(X)098163213732104525886151713381059168∑i=09Xi=1205

μ=∑i=1nXin=120510=120.5

Hence, the population mean is 120.5.

Answer 13

(b)

To determine

The simple random sample of size 3.

(b)

Expert Solution

Answer to Problem 27E

Solution: The selected simple random sample is the players numbered 1, 9, and 2.

Explanation of Solution

There are nine players numbered 0,1…9. The players in this study are selected using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column. The random number is selected between 0 and 9. The obtained samples are 1, 9, and 2. The players who have the same numbers with the selected random numbers will be included in the sample.

Answer 14

(b)

To determine

The simple random sample of size 3.

Answer 15

(b)

Expert Solution

Answer to Problem 27E

Solution: The selected simple random sample is the players numbered 1, 9, and 2.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

There are nine players numbered 0,1…9. The players in this study are selected using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column. The random number is selected between 0 and 9. The obtained samples are 1, 9, and 2. The players who have the same numbers with the selected random numbers will be included in the sample.

Answer 20

To determine

The sample mean.

Expert Solution

Answer to Problem 27E

Solution: The sample mean is 122.67_.

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=63+168+1373=3683=122.67

The sample mean of sample observations 1, 9, and 2 is 122.67.

Answer 21

To determine

The sample mean.

Answer 22

Expert Solution

Answer to Problem 27E

Solution: The sample mean is 122.67_.

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=63+168+1373=3683=122.67

The sample mean of sample observations 1, 9, and 2 is 122.67.

Answer 27

(c)

To determine

The simple random samples of size 3 nine times.

(c)

Expert Solution

Answer to Problem 27E

Solution: The simple random samples obtained are

(9,5,0),(0,5,7),(2,8,7),(9,6,4),(1,2,5),(4,2,5),(8,2,8),(7,3,6),(4,7,1)_

Explanation of Solution

There are nine players numbered 0,1,..,9. The players in this study are chosen using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column of the table. The random number is selected between 0 and 9. The obtained samples are 9, 5, and 0. The players who have the same numbers with the selected random numbers are included in the sample. The remaining eight samples are drawn in the similar manner.

Hence, the table of all the 10 samples obtained is drawn as

Sample numberSample observations1(1,9,2)2(9,5,0)3(0,5,7)4(2,8,7)5(9,6,4)6(1,2,5)7(4,2,5)8(8,2,8)9(7,3,6)10(4,7,1)

Answer 28

(c)

To determine

The simple random samples of size 3 nine times.

Answer 29

(c)

Expert Solution

Answer to Problem 27E

Solution: The simple random samples obtained are

(9,5,0),(0,5,7),(2,8,7),(9,6,4),(1,2,5),(4,2,5),(8,2,8),(7,3,6),(4,7,1)_

Answer 30

(c)

Expert Solution

Answer 31

(c)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

There are nine players numbered 0,1,..,9. The players in this study are chosen using the random number table provided in the book. The three random numbers of one digit are chosen from the random number table, starting from the 101st row and the first column of the table. The random number is selected between 0 and 9. The obtained samples are 9, 5, and 0. The players who have the same numbers with the selected random numbers are included in the sample. The remaining eight samples are drawn in the similar manner.

Hence, the table of all the 10 samples obtained is drawn as

Sample numberSample observations1(1,9,2)2(9,5,0)3(0,5,7)4(2,8,7)5(9,6,4)6(1,2,5)7(4,2,5)8(8,2,8)9(7,3,6)10(4,7,1)

Answer 34

To determine

The sample mean of the simple random samples drawn above.

Expert Solution

Answer to Problem 27E

Solution: The sample mean for each simple random sample is shown in the table below.

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=168+88+983=118

The sample means for 10 random samples are computed in a similar way. The table showing calculation for the computation of the sample mean is drawn below:

Sample numberSimple random samples Sample ObservationsSample mean11,9,263,168,13763+168+1373=122.6729,5,0168,88,98168+88+983=11830,5,798,88,13398+88+1333=106.3342,8,7137,105,133137+105+1333=12559,6,4168,151,52168+151+523=123.6761,2,563,137,8863+137+883=9674,2,552,137,5552+137+553=81.3388,2,8105,137,105105+137+1053=115.6797,3,6133,210,151133+210+1513=164.67104,7,152,133,6352+133+633=82.67

Answer 35

To determine

The sample mean of the simple random samples drawn above.

Answer 36

Expert Solution

Answer to Problem 27E

Solution: The sample mean for each simple random sample is shown in the table below.

Answer 37

Expert Solution

Answer 38

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

The sample mean is calculated as

X¯=∑i=1n=3Xin=168+88+983=118

The sample means for 10 random samples are computed in a similar way. The table showing calculation for the computation of the sample mean is drawn below:

Sample numberSimple random samples Sample ObservationsSample mean11,9,263,168,13763+168+1373=122.6729,5,0168,88,98168+88+983=11830,5,798,88,13398+88+1333=106.3342,8,7137,105,133137+105+1333=12559,6,4168,151,52168+151+523=123.6761,2,563,137,8863+137+883=9674,2,552,137,5552+137+553=81.3388,2,8105,137,105105+137+1053=115.6797,3,6133,210,151133+210+1513=164.67104,7,152,133,6352+133+633=82.67

Answer 41

To determine

To graph: The histogram showing the 10 values of sample mean.

Expert Solution

Explanation of Solution

The histogram showing the values of 10 sample mean is drawn in Minitab. The steps are written below:

Step 1. Enter the data in Minitab classifying the sample mean of 10 samples.

Step 2. Click on Graph in toolbox and click on histogram.

Step 3. Next, choose simple histogram option appearing in the dialog box and click OK.

Step 4. Drag the sample mean appearing on the left side in Graph variables and click on OK..

Graph: The obtained histogram showing the frequency and sample mean is as follows:

Introduction to the Practice of Statistics, Chapter 5.2, Problem 27E

Answer 42

To determine

To graph: The histogram showing the 10 values of sample mean.

Answer 43

Expert Solution

Explanation of Solution

The histogram showing the values of 10 sample mean is drawn in Minitab. The steps are written below:

Step 1. Enter the data in Minitab classifying the sample mean of 10 samples.

Step 2. Click on Graph in toolbox and click on histogram.

Step 3. Next, choose simple histogram option appearing in the dialog box and click OK.

Step 4. Drag the sample mean appearing on the left side in Graph variables and click on OK..

Graph: The obtained histogram showing the frequency and sample mean is as follows:

Introduction to the Practice of Statistics, Chapter 5.2, Problem 27E

Answer 44

Expert Solution

Answer 45

Expert Solution

Answer 46

Expert Solution

Answer 47

(d)

To determine

Whether the center of the histogram is close to population mean.

(d)

Expert Solution

Answer to Problem 27E

Solution: The center of the histogram is close to population mean.

Explanation of Solution

The histogram drawn in part (c) shows that the sample means of 10 samples are close to 120 and the population mean computed in part (a) is equal to 120.5. This shows that the population mean is approximately equal to the sample means obtained by drawing 10 simple random samples from the population.

Answer 48

(d)

To determine

Whether the center of the histogram is close to population mean.

Answer 49

(d)

Expert Solution

Answer to Problem 27E

Solution: The center of the histogram is close to population mean.

Answer 50

(d)

Expert Solution

Answer 51

(d)

Expert Solution

Answer 52

Expert Solution

Answer 53

Explanation of Solution

The histogram drawn in part (c) shows that the sample means of 10 samples are close to 120 and the population mean computed in part (a) is equal to 120.5. This shows that the population mean is approximately equal to the sample means obtained by drawing 10 simple random samples from the population.