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.

Question

Want to see more full solutions like this?

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).

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!

Students have asked these similar questions

In order to find probability, you can use this formula in Microsoft Excel: The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest. =NORM.DIST(x, Mean, Standard Dev., TRUE). When the question mentions “greater than” you may have to subtract your answer from 1. When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer. 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…

If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…

Problem 1: The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is: Between the mean and $45 per hour? More than $45 per hour? Less than $32 per hour? Problem 2: The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the probability of randomly selecting a value less than 395 pounds? Problem 3: In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution. What percent of New York State high school teachers earn between 70,000 and 75,000? What percent of New York State high school…

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).

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

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).

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 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).

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

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

Ch. 8.1 - A simple random sample of 40 items resulted in a...Ch. 8.1 - 2. A simple random sample of 50 items from a...Ch. 8.1 - A simple random sample of 60 items resulted in a...Ch. 8.1 - 4. A 95% confidence interval for a population mean...Ch. 8.1 - Data were collected on the amount spent by 64...Ch. 8.1 - Travel Taxes. In an attempt to assess total daily...Ch. 8.1 - Cost of Dog Ownership. Money reports that the...Ch. 8.1 - Studies show that massage therapy has a variety of...Ch. 8.1 - Cost to Repair Fire Damage. The mean cost to...Ch. 8.1 - 10. Costs are rising for all kinds of medical...

Videos

Answer to Problem 48SE

Explanation of Solution

Answer to Problem 48SE

Explanation of Solution

Want to see more full solutions like this?

Chapter 8 Solutions