Question 1

The mean of fifty sales receipts is $65.75 and the standard deviation is $10.55.Using Chebysheff's Theorem,75% of the sales receipts were between $44.65 and $86.85.

Accepted Answer

Using Chebyshev's Theorem, we know that at least (1 - 1/k^2) of the data points will fall within k standard deviations from the mean, where k is any positive integer greater than 1.

For example, if we let k=2, then we know that at least 1 - 1/2^2 = 75% of the data points will fall within 2 standard deviations from the mean.

Given that the mean of the sales receipts is $65.75 and the standard deviation is $10.55, we can calculate the range within 2 standard deviations from the mean:

$65.75 - 2($10.55) = $44.65 
$65.75 + 2($10.55) = $86.85

Therefore, using Chebyshev's Theorem, we can conclude that at least 75% of the sales receipts fall within the range of $44.65 and $86.85.

Thus, the statement is true and the answer is A.

Question 2

Suppose that a firm's sales were $3,750,000 five years ago and are $5,250,000 today.What was the geometric mean growth rate in sales over the past five years?

Accepted Answer

The answer of Suppose that a firm's sales were $3,750,000...

Question 3

Ages of Senior Citizens ​ A sociologist recently conducted a survey of citizens over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 22 uninsured senior citizens were as follows: 65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,81,86,87,91,92, 94,and 97. ​ ​
-{Ages of Senior Citizens Narrative} Explain why there is no mode for this data set.

Accepted Answer

The answer of Ages of Senior Citizens ​ A sociologist...

Question 4

The difference between the largest and smallest observations in an ordered data set is called the range.

Accepted Answer

The definition given in the statement is correct, so the answer is true.

Question 5

Ages of Senior Citizens ​ A sociologist recently conducted a survey of citizens over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 22 uninsured senior citizens were as follows: 65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,81,86,87,91,92, 94,and 97. ​ ​
-{Ages of Senior Citizens Narrative} Calculate the mean age of the uninsured senior citizens

Accepted Answer

The answer of Ages of Senior Citizens ​ A sociologist...

Question 6

2-Year Investment ​ Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000. ​ ​
-{2-Year Investment Narrative} Calculate the arithmetic mean.

Accepted Answer

The answer of  2-Year Investment ​ Suppose you make...

Question 7

While Chebysheff's Theorem applies to any distribution,regardless of shape,the Empirical Rule applies only to distributions that are bell shaped.

Accepted Answer

Chebysheff's Theorem is a general theorem that applies to any distribution, while the Empirical Rule only applies to bell-shaped distributions. Therefore, the statement is true.

Question 8

2-Year Investment ​ Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000. ​ ​
-{2-Year Investment Narrative} Compare the values of the arithmetic and geometric means.

Accepted Answer

The answer of  2-Year Investment ​ Suppose you make...

Question 9

The standard deviation is expressed in terms of the original units of measurement but the variance is not.

Accepted Answer

The standard deviation is the square root of the variance, thus it is expressed in the original units of measurement, whereas the variance is expressed in squared units.

Question 10

2-Year Investment ​ Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000. ​ ​
-{2-Year Investment Narrative} Calculate the geometric mean.

Accepted Answer

The answer of  2-Year Investment ​ Suppose you make...

Question 11

A mutual fund you purchased in the years 2011-2014 has the following rates of return shown below:  Compute the geometric mean.

Accepted Answer

The answer of A mutual fund you purchased in the...

Question 12

The mean of a sample of 15 measurements is 35.6 feet.Suppose that the sample is enlarged to 16
measurements,by including one additional measurement having a value of 42 feet.Find the mean of
the sample of the 16 measurements.

Accepted Answer

The answer of The mean of a sample of 15...

Question 13

A sample of 12 construction workers has a mean age of 25 years.Suppose that the sample is enlarged
to 14 construction workers,by including two additional workers having common age of 25 each.
Find the mean of the sample of 14 workers.

Accepted Answer

The answer of A sample of 12 construction workers has...

Question 14

The data set 10,20,30 has the same variance as the data set 100,200,300.

Accepted Answer

The variance of a data set is affected by the scale of the numbers. The data set 100, 200, 300 has a larger variance than 10, 20, 30 because the numbers are scaled up by a factor of 10.

Question 15

Ages of Senior Citizens ​ A sociologist recently conducted a survey of citizens over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 22 uninsured senior citizens were as follows: 65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,81,86,87,91,92, 94,and 97. ​ ​
-{Ages of Senior Citizens Narrative} Calculate the median age of the uninsured senior citizens.

Accepted Answer

The answer of Ages of Senior Citizens ​ A sociologist...

Question 16

According to Chebysheff's Theorem,at least 93.75% of observations should fall within 4 standard deviations of the mean.

Accepted Answer

Chebysheff's theorem states that for any data set, regardless of distribution, at least 1 - 1/k^2 of the data will fall within k standard deviations of the mean. Therefore, for k = 2, at least 75% of observations will fall within 2 standard deviations of the mean, for k = 3, at least 88.89% of observations will fall within 3 standard deviations of the mean, and for k = 4, at least 93.75% of observations will fall within 4 standard deviations of the mean.

Question 17

Suppose that a firm's sales were $2,500,000 four years ago,and sales have grown annually by 25%,
15%,−5%,and 10% since that time.What was the geometric mean growth rate in sales over the past
four years?

Accepted Answer

The answer of Suppose that a firm's sales were $2,500,000...

Question 18

The value of the standard deviation may be either positive or negative,while the value of the variance will always be positive.

Accepted Answer

This statement is incorrect. The variance can be negative in certain situations, such as when dealing with a biased sample. However, in most practical situations, the variance is positive.

Question 19

σ is a population parameter and s is a sample statistic.

Accepted Answer

σ represents the population standard deviation, while s represents the sample standard deviation. Therefore, σ is a population parameter and s is a sample statistic.

Question 20

Chebysheff's Theorem states that the percentage of observations in a data set that should fall within five standard deviations of their mean is at least 96%.

Accepted Answer

Chebysheff's Theorem states that regardless of the shape of the distribution, at least 1 - (1/k^2) of the observations in a data set will fall within k standard deviations of the mean. When k=5, 1 - (1/5^2) = 96%, so at least 96% of the observations will fall within five standard deviations of the mean.

Quiz 4: Numerical Descriptive Techniques

The mean of fifty sales receipts is $65.75 and the standard deviation is $10.55.Using Chebysheff's Theorem,75% of the sales receipts were between $44.65 and $86.85.

Suppose that a firm's sales were $3,750,000 five years ago and are $5,250,000 today.What was the geometric mean growth rate in sales over the past five years?

The difference between the largest and smallest observations in an ordered data set is called the range.

2-Year Investment Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000. -{2-Year Investment Narrative} Calculate the arithmetic mean.

While Chebysheff's Theorem applies to any distribution,regardless of shape,the Empirical Rule applies only to distributions that are bell shaped.

The standard deviation is expressed in terms of the original units of measurement but the variance is not.

2-Year Investment Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000. -{2-Year Investment Narrative} Calculate the geometric mean.

A mutual fund you purchased in the years 2011-2014 has the following rates of return shown below: Compute the geometric mean.

The mean of a sample of 15 measurements is 35.6 feet.Suppose that the sample is enlarged to 16 measurements,by including one additional measurement having a value of 42 feet.Find the mean of the sample of the 16 measurements.

A sample of 12 construction workers has a mean age of 25 years.Suppose that the sample is enlarged to 14 construction workers,by including two additional workers having common age of 25 each. Find the mean of the sample of 14 workers.

The data set 10,20,30 has the same variance as the data set 100,200,300.

According to Chebysheff's Theorem,at least 93.75% of observations should fall within 4 standard deviations of the mean.

Suppose that a firm's sales were $2,500,000 four years ago,and sales have grown annually by 25%, 15%,−5%,and 10% since that time.What was the geometric mean growth rate in sales over the past four years?

The value of the standard deviation may be either positive or negative,while the value of the variance will always be positive.

σ is a population parameter and s is a sample statistic.

Chebysheff's Theorem states that the percentage of observations in a data set that should fall within five standard deviations of their mean is at least 96%.

Quiz 4: Numerical Descriptive Techniques

The mean of fifty sales receipts is $65.75 and the standard deviation is $10.55.Using Chebysheff's Theorem,75% of the sales receipts were between $44.65 and $86.85.

Suppose that a firm's sales were $3,750,000 five years ago and are $5,250,000 today.What was the geometric mean growth rate in sales over the past five years?

The difference between the largest and smallest observations in an ordered data set is called the range.

2-Year Investment ​ Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000. ​ ​ -{2-Year Investment Narrative} Calculate the arithmetic mean.

While Chebysheff's Theorem applies to any distribution,regardless of shape,the Empirical Rule applies only to distributions that are bell shaped.

The standard deviation is expressed in terms of the original units of measurement but the variance is not.

2-Year Investment ​ Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000. ​ ​ -{2-Year Investment Narrative} Calculate the geometric mean.

A mutual fund you purchased in the years 2011-2014 has the following rates of return shown below: Compute the geometric mean.

The mean of a sample of 15 measurements is 35.6 feet.Suppose that the sample is enlarged to 16 measurements,by including one additional measurement having a value of 42 feet.Find the mean of the sample of the 16 measurements.

A sample of 12 construction workers has a mean age of 25 years.Suppose that the sample is enlarged to 14 construction workers,by including two additional workers having common age of 25 each. Find the mean of the sample of 14 workers.

The data set 10,20,30 has the same variance as the data set 100,200,300.

According to Chebysheff's Theorem,at least 93.75% of observations should fall within 4 standard deviations of the mean.

Suppose that a firm's sales were $2,500,000 four years ago,and sales have grown annually by 25%, 15%,−5%,and 10% since that time.What was the geometric mean growth rate in sales over the past four years?

The value of the standard deviation may be either positive or negative,while the value of the variance will always be positive.

σ is a population parameter and s is a sample statistic.

Chebysheff's Theorem states that the percentage of observations in a data set that should fall within five standard deviations of their mean is at least 96%.

2-Year Investment Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000. -{2-Year Investment Narrative} Calculate the arithmetic mean.

2-Year Investment Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000. -{2-Year Investment Narrative} Calculate the geometric mean.