Question 1

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 recently conducted...

Question 2

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

This statement is true. Chebyshev's Theorem states that no matter what the shape of the distribution is, at least 1 - (1/k^2) of the data will fall within k standard deviations of the mean, where k is any positive number greater than 1. When k=5, we get 1-1/25 or at least 96% observations falling within 5 standard deviations of the mean.

Question 3

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 a 2-year investment...

Question 4

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

Accepted Answer

This statement is true.

Question 5

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

Accepted Answer

This statement is true. The Empirical Rule is also known as the 68-95-99.7 Rule, and it only applies to distributions that are approximately bell-shaped, meaning that they are roughly symmetric and have a single peak. On the other hand, Chebyshev's Theorem applies to any distribution, regardless of its shape.

Question 6

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

Accepted Answer

The answer of The data set 10,20,30 has the same...

Question 7

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 8

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 recently conducted...

Question 9

$\sigma$ is a population parameter and s is a sample statistic.

Accepted Answer

F1F1F1S1F1F1F10 is a population parameter because it describes the entire population, while s is a sample statistic because it describes only a sample of the population.

Question 10

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

Accepted Answer

Chebyshev's Theorem states that at least 1-1/k^2 of the observations will fall within k standard deviations of the mean, where k is any value greater than 1. Plugging in k=4, we get that at least 1 - 1/4^2 = 0.9375, which is equivalent to 93.75%. Therefore, at least 93.75% of observations should fall within 4 standard deviations of the mean.

Question 11

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

Accepted Answer

The variance can never be negative, but the standard deviation can be either positive or negative depending on the distribution. However, the value reported as the standard deviation is always the positive square root of the variance.

Question 12

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 a 2-year investment...

Question 13

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 14

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 15

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 a 2-year investment...

Question 16

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 17

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 18

A mutual fund you purchased in the years 2011-2014 has the following rates of return shown below:
 $$\begin{array} { | l | c | c | c | c | } 
\hline \text { Year } & 2011 & 2012 & 2013 & 2014 \
\hline \text { Rate of Return } & .50 & .30 & - .10 & - .15 \
\hline
\end{array}$$ Compute the geometric mean.

Accepted Answer

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

Question 19

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

Chebyshev's Theorem states that for any data set at least (1 - 1/k^2) of the data values will be within k standard deviations of the mean, where k is a constant greater than 1.

In this case, k can be found by solving for the interval that contains 75% of the data:

75% = (1-1/k^2)
1/k^2 = 0.25
k = sqrt(4) = 2

Therefore, according to Chebyshev's Theorem, at least 75% of the data fall within 2 standard deviations of the mean.

Using the mean and standard deviation provided, we can calculate the interval that contains 2 standard deviations:

Lower bound = mean - (2 x standard deviation) 
Lower bound = $65.75 - (2 x $10.55) = $44.65

Upper bound = mean + (2 x standard deviation) 
Upper bound = $65.75 + (2 x $10.55) = $86.85

So given that we know at least 75% of the data falls within 2 standard deviations of the mean, and the interval that contains 2 standard deviations includes the range from $44.65 to $86.85, the statement is true.

Question 20

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 recently conducted...

Quiz 4: A: Numerical Descriptive Techniques

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 geometric mean.

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

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

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

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.

$\sigma$ is a population parameter and s is a sample statistic.

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

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

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?

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.

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.

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

A mutual fund you purchased in the years 2011-2014 has the following rates of return shown below: $\begin{array} { | l | c | c | c | c | } \hline \text { Year } & 2011 & 2012 & 2013 & 2014 \\\hline \text { Rate of Return } & .50 & .30 & - .10 & - .15 \\\hline\end{array}$ Compute the geometric mean.

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.

Quiz 4: A: Numerical Descriptive Techniques

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 geometric mean.

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

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

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

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.

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

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

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

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?

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.

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.

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

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.

$\sigma$ is a population parameter and s is a sample statistic.