The standard deviations of the 2 random variables are σH=1.421 and σF=1.249.. Explain why this difference makes sense.

Jaya Legge 2021-08-08 Answered

In government data, a house-hold consists of all occupants of a dwelling unit, while a family consists of 2 or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size and family size in the United States.
\( \begin{array}{||c|c|c|c|c|c|c|} \hline \text{Number of people}& 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \begin{array}{l} \text { Household } \ \text { probability } \end{array} & 0.25 & 0.32 & 0.17 & 0.15 & 0.07 & 0.03 & 0.01 \\ \hline \begin{array}{l} \text { Family } \ \text { probability } \end{array} & 0 & 0.42 & 0.23 & 0.21 & 0.09 & 0.03 & 0.02 \\ \hline \end{array}\)
Let H = the number of people in a randomly selected U.S. household and F = the number of people in a randomly chosen U.S. family. The standard deviations of the 2 random variables are σH=1.421 and σF=1.249.. Explain why this difference makes sense.

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

pierretteA
Answered 2021-08-09 Author has 15843 answers
Given:
Household σ = 1.421
Family σ = 1.249
In part (a), we concluded that the spread of the household distribution was greater than the spread of the family distribution, becatise the histogram of the household distribution is wider.
This is confirmed hy the standard deviations, hecausethe standard deviation of household is greater than the standard deviation of family.
Moreover, this also makes sense, becatise a hotischold can contain 1 individual but a family always needs to contain more than 1 individual and thus there are more possible values for the number of individuals in a household (making its standard deviation greater).
Have a similar question?
Ask An Expert
30
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-08-08

In government data, a household consists of all occupants of a dwelling unit, while a family consists of 2 or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size and family size in the United States.
\( \begin{array}{||c|c|c|c|c|c|c|} \hline \text{Number of people}& 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \begin{array}{l} \text { Household } \ \text { probability } \end{array} & 0.25 & 0.32 & 0.17 & 0.15 & 0.07 & 0.03 & 0.01 \\ \hline \begin{array}{l} \text { Family } \ \text { probability } \end{array} & 0 & 0.42 & 0.23 & 0.21 & 0.09 & 0.03 & 0.02 \\ \hline \end{array}\)
Let H = the number of people in a randomly selected U.S. household and F = the number of people in a randomly chosen U.S. family. Find the expected value of each random variable. Explain why this difference makes sense.

asked 2021-05-11

Determine whether each statement makes sense or does not make sense, and explain your reasoning. A system of linear equations in three variables, x, y, and z cannot contain an equation in the form \(y = mx + b\).

asked 2021-06-01

Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: \(X+Y\)

asked 2021-05-27
Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 0.5Y
asked 2021-05-18
Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: X-20
asked 2021-05-14
When σ is unknown and the sample size is \(\displaystyle{n}\geq{30}\), there are tow methods for computing confidence intervals for μμ. Method 1: Use the Student's t distribution with d.f. = n - 1. This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method. Method 2: When \(\displaystyle{n}\geq{30}\), use the sample standard deviation s as an estimate for σσ, and then use the standard normal distribution. This method is based on the fact that for large samples, s is a fairly good approximation for σσ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution. Consider a random sample of size n = 31, with sample mean x¯=45.2 and sample standard deviation s = 5.3. (c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?
asked 2021-05-22
Sheila is in Ms. Cai's class . She noticed that the graph of the perimeter for the "dented square" in problem 3-61 was a line . "I wonder what the graph of its area looks like ," she said to her teammates .
a. Write an equation for the area of the "dented square" if xx represents the length of the large square and yy represents the area of the square.
b. On graph paper , graph the rule you found for the area in part (a). Why does a 1st−quadrant graph make sense for this situation? Are there other values of xx that cannot work in this situation? Be sure to include an indication of this on your graph, as necessary.
c. Explain to Sheila what the graph of the area looks like.
d. Use the graph to approximate xx when the area of the shape is 20 square units.
...