A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.77. The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15. a. Using the sample data, what is the margin of error associated with a 95% confidence interval? b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share.

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Answer 1

Textbook Question

Chapter 8, Problem 48SE

A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.77. The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.

a. Using the sample data, what is the margin of error associated with a 95% confidence interval?
b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share.

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

Find the margin of error for 95% confidence level.

Answer to Problem 48SE

The margin of error for 95% confidence level is 4.

Explanation of Solution

Calculation:

The given information is that the sample of 54 discount brokers shows the mean price of the trade is $50 for 100 shares is $33.77 and the population standard deviation is $15.

The formula for margin of error is zα2σn.

From the “Table 8.1 value of zα2”, the value of zα2 for 95% is 1.96.

The value of margin of error is

zα2σn=1.961554=1.96×2.04=4

Thus, the value of margin of error is 4.

b.

Expert Solution

To determine

Find the 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share.

Answer to Problem 48SE

The 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77, $37.77).

Explanation of Solution

Calculation:

From part (a), the margin of error is 4.

The mean value for the 54 broker for trade of 100 shares at $50 per share is $33.77.

The value of confidence interval for population mean is

x¯±zα2σn=33.77±4=(33.77−4,33.77+4)=(29.77,37.77)

Thus, the 95% confidence interval for population mean is ($29.77, $37.77).

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Answer 2

Textbook Question

Chapter 8, Problem 48SE

A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.77. The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.

a. Using the sample data, what is the margin of error associated with a 95% confidence interval?
b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share.

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

Find the margin of error for 95% confidence level.

Answer to Problem 48SE

The margin of error for 95% confidence level is 4.

Explanation of Solution

Calculation:

The given information is that the sample of 54 discount brokers shows the mean price of the trade is $50 for 100 shares is $33.77 and the population standard deviation is $15.

The formula for margin of error is zα2σn.

From the “Table 8.1 value of zα2”, the value of zα2 for 95% is 1.96.

The value of margin of error is

zα2σn=1.961554=1.96×2.04=4

Thus, the value of margin of error is 4.

b.

Expert Solution

To determine

Find the 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share.

Answer to Problem 48SE

The 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77, $37.77).

Explanation of Solution

Calculation:

From part (a), the margin of error is 4.

The mean value for the 54 broker for trade of 100 shares at $50 per share is $33.77.

The value of confidence interval for population mean is

x¯±zα2σn=33.77±4=(33.77−4,33.77+4)=(29.77,37.77)

Thus, the 95% confidence interval for population mean is ($29.77, $37.77).

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Answer 3

Textbook Question

Chapter 8, Problem 48SE

A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.77. The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.

a. Using the sample data, what is the margin of error associated with a 95% confidence interval?
b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share.

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

Find the margin of error for 95% confidence level.

Answer to Problem 48SE

The margin of error for 95% confidence level is 4.

Explanation of Solution

Calculation:

The given information is that the sample of 54 discount brokers shows the mean price of the trade is $50 for 100 shares is $33.77 and the population standard deviation is $15.

The formula for margin of error is zα2σn.

From the “Table 8.1 value of zα2”, the value of zα2 for 95% is 1.96.

The value of margin of error is

zα2σn=1.961554=1.96×2.04=4

Thus, the value of margin of error is 4.

b.

Expert Solution

To determine

Find the 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share.

Answer to Problem 48SE

The 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77, $37.77).

Explanation of Solution

Calculation:

From part (a), the margin of error is 4.

The mean value for the 54 broker for trade of 100 shares at $50 per share is $33.77.

The value of confidence interval for population mean is

x¯±zα2σn=33.77±4=(33.77−4,33.77+4)=(29.77,37.77)

Thus, the 95% confidence interval for population mean is ($29.77, $37.77).

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Answer 4

Textbook Question

Chapter 8, Problem 48SE

A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.77. The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.

a. Using the sample data, what is the margin of error associated with a 95% confidence interval?
b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share.

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

Find the margin of error for 95% confidence level.

Answer to Problem 48SE

The margin of error for 95% confidence level is 4.

Explanation of Solution

Calculation:

The given information is that the sample of 54 discount brokers shows the mean price of the trade is $50 for 100 shares is $33.77 and the population standard deviation is $15.

The formula for margin of error is zα2σn.

From the “Table 8.1 value of zα2”, the value of zα2 for 95% is 1.96.

The value of margin of error is

zα2σn=1.961554=1.96×2.04=4

Thus, the value of margin of error is 4.

b.

Expert Solution

To determine

Find the 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share.

Answer to Problem 48SE

The 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77, $37.77).

Explanation of Solution

Calculation:

From part (a), the margin of error is 4.

The mean value for the 54 broker for trade of 100 shares at $50 per share is $33.77.

The value of confidence interval for population mean is

x¯±zα2σn=33.77±4=(33.77−4,33.77+4)=(29.77,37.77)

Thus, the 95% confidence interval for population mean is ($29.77, $37.77).

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

Find the margin of error for 95% confidence level.

Answer to Problem 48SE

The margin of error for 95% confidence level is 4.

Explanation of Solution

Calculation:

The given information is that the sample of 54 discount brokers shows the mean price of the trade is $50 for 100 shares is $33.77 and the population standard deviation is $15.

The formula for margin of error is zα2σn.

From the “Table 8.1 value of zα2”, the value of zα2 for 95% is 1.96.

The value of margin of error is

zα2σn=1.961554=1.96×2.04=4

Thus, the value of margin of error is 4.

b.

Expert Solution

To determine

Find the 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share.

Answer to Problem 48SE

The 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77, $37.77).

Explanation of Solution

Calculation:

From part (a), the margin of error is 4.

The mean value for the 54 broker for trade of 100 shares at $50 per share is $33.77.

The value of confidence interval for population mean is

x¯±zα2σn=33.77±4=(33.77−4,33.77+4)=(29.77,37.77)

Thus, the 95% confidence interval for population mean is ($29.77, $37.77).

Answer 8

a.

Expert Solution

To determine

Find the margin of error for 95% confidence level.

Answer to Problem 48SE

The margin of error for 95% confidence level is 4.

Explanation of Solution

Calculation:

The given information is that the sample of 54 discount brokers shows the mean price of the trade is $50 for 100 shares is $33.77 and the population standard deviation is $15.

The formula for margin of error is zα2σn.

From the “Table 8.1 value of zα2”, the value of zα2 for 95% is 1.96.

The value of margin of error is

zα2σn=1.961554=1.96×2.04=4

Thus, the value of margin of error is 4.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Find the margin of error for 95% confidence level.

Answer 13

Answer to Problem 48SE

The margin of error for 95% confidence level is 4.

Answer 14

Explanation of Solution

Calculation:

The given information is that the sample of 54 discount brokers shows the mean price of the trade is $50 for 100 shares is $33.77 and the population standard deviation is $15.

The formula for margin of error is zα2σn.

From the “Table 8.1 value of zα2”, the value of zα2 for 95% is 1.96.

The value of margin of error is

zα2σn=1.961554=1.96×2.04=4

Thus, the value of margin of error is 4.

Answer 15

b.

Expert Solution

To determine

Find the 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share.

Answer to Problem 48SE

The 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77, $37.77).

Explanation of Solution

Calculation:

From part (a), the margin of error is 4.

The mean value for the 54 broker for trade of 100 shares at $50 per share is $33.77.

The value of confidence interval for population mean is

x¯±zα2σn=33.77±4=(33.77−4,33.77+4)=(29.77,37.77)

Thus, the 95% confidence interval for population mean is ($29.77, $37.77).

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Find the 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share.

Answer 20

Answer to Problem 48SE

The 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77, $37.77).

Answer 21

Explanation of Solution

Calculation:

From part (a), the margin of error is 4.

The mean value for the 54 broker for trade of 100 shares at $50 per share is $33.77.

The value of confidence interval for population mean is

x¯±zα2σn=33.77±4=(33.77−4,33.77+4)=(29.77,37.77)

Thus, the 95% confidence interval for population mean is ($29.77, $37.77).

Answer 22

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