Question

In: Statistics and Probability

The Census Bureau gives this distribution for the number of people in American households in a...

The Census Bureau gives this distribution for the number of people in American households in a certain year.

Family Size	Proportion
1	0.29
2	0.34
3	0.15
4	0.13
5	0.06
6	0.02
7	0.01

Note: In this table, 7 actually represents households of size 7 or greater. But for purposes of this exercise, assume that it means only households of size exactly 7.)

(a)

This is also the probability distribution for the size of randomly chosen households. The expected value of this distribution is the average number of people in a household. What is this expected value?

people

(b)

Suppose you take a random sample of 1,000 American households. About how many of these households will be of size 2?

households

About how many of these households will be of sizes 3 to 7?

households

(c)

Based on your calculations in part (b), how many people are represented in your sample of 1,000 households? (Hint: The number of individuals in your sample who live in households of size 7 is 7 times the number of households of size 7. Repeat this reasoning to determine the number of individuals in households of sizes 1 to 6. Add the results to get the total number of people represented in your sample.)

people

Calculate the probability distribution for the household size lived in by individual people. (Round your answers to four decimal places.)

Family Size	Proportion
1
2
3
4
5
6
7

Describe the shape of this distribution. What does this shape tell you about household structure? (Round your mean to one decimal place.)

The distribution is ---Select--- left skewed symmetric right skewed , with a median of and a mean of around people.

Expert Solution

Distribution

It is negatively skewed

Median is less than mean

Excel calculaitons are as follows

orchestra answered 2 years ago

According to the Census bureau the distribution by ethnic background of the NYC population in a...

According to the Census bureau the distribution by ethnic background of the NYC population in a recent year was Hispanic 28% Black 24% White 35% Asian 12% Others 1% The manager of a large complex in the city wonders whether the distribution by race of the complex's resident is consistent with the population distribution. To find out, she records data from random sample of 800 residents. Table below displays sample data. α=0.05 Race hispanic black white asian others count 212...

Question 5 (1 point) Saved A U.S. census bureau pollster noted that in 447 random households...

Question 5 (1 point) Saved A U.S. census bureau pollster noted that in 447 random households surveyed, 290 occupants owned their own home. What is the 99% confidence interval estimate of the proportion of American households who own their own home? Question 5 options: 1) ( 0.62619 , 0.67135 ) 2) ( 0.59061 , 0.70693 ) 3) ( 0.59625 , 0.70129 ) 4) ( -0.59061 , 0.70693 ) 5) ( 0.29307 , 0.40939 ) Question 6 (1 point) You work...

Over the past several years, the proportion of one-person households has been increasing. The Census Bureau...

Over the past several years, the proportion of one-person households has been increasing. The Census Bureau would like to test the hypothesis that the proportion of one-person households exceeds 0.27. A random sample of 125 households found that 43 consisted of one person. The Census Bureau would like to set α = 0.05. Use the critical value approach to test this hypothesis

Changes in Education Attainment: USE SOFTWARE - According to the U.S. Census Bureau, the distribution of...

Changes in Education Attainment: USE SOFTWARE - According to the U.S. Census Bureau, the distribution of Highest Education Attainment in U.S. adults aged 25 - 34 in the year 2005 is given in the table below. Census: Highest Education Attainment - 2005 No High School Associate's Bachelor's Graduate or Diploma Diploma Degree Degree Professional Degree Percent 14% 48% 8% 22% 8% In a survey of 4000 adults aged 25 - 34 in the year 2013, the counts for these levels...

According to the Census Bureau, the distribution by ethnic background of the New York City population...

According to the Census Bureau, the distribution by ethnic background of the New York City population in a recent year was Hispanic: 28% Black: 24% White: 35% Asian: 12% Others: 1% The manager of a large housing complex in the city wonders whether the distribution byrace of the complex’s residents is consistent with the population distribution. To find out,she records data from random sample of 800 residents. The table below displays the sample data. Race Hispanic Black White Asian Others...

12.10 What’s the average? The Census Bureau website gives several choices for ‘‘average income’’ in its...

12.10 What’s the average? The Census Bureau website gives several choices for ‘‘average income’’ in its historical income data. In 2013, the median income of American households was $51,939. The mean household income was $72,641. The median income of families was $63,815, and the mean family income was $84,687. The Census Bureau says, “Households consist of all people who occupy a housing unit. The term ‘family’ refers to a group of two or more people related by birth, marriage, or...

A statewide census examined the number of beds in households and reported a mean (μ) of...

A statewide census examined the number of beds in households and reported a mean (μ) of 2.25 beds and standard deviation (σ) of 1.9 beds per household. But, since I live in a neighborhood with larger families, I have a hunch that the average number of beds in households will be higher in my neighborhood. To test this idea, I randomly picked 25 families in my neighborhood and surveyed them on the number of beds in their home. I would...

In reference to the year 2000 national census, the distribution of United States households according to...

In reference to the year 2000 national census, the distribution of United States households according to type of living arrangement is given in the table below. An SRS of 500 households gives the observed frequencies, by household type, for the city of Aurora, Illinois. Ethnic Origin Census Percent Observed frequency from sample Married, with children 25% 95 Married, with no children 20% 110 Single parent 5% 35 Single individual 15% 65 One person 20% 120 Other (roommate,...

Measures of Average: U.S. Census Bureau The U.S. Census Bureau reports the median family income in...

Measures of Average: U.S. Census Bureau The U.S. Census Bureau reports the median family income in its summary of census data. a) Why do you suppose it uses the median instead of the mean? b) What might be the disadvantages of reporting the mean? Measures of Variation: MP3 Player Life Span A company selling a new MP3 player advertises that the player has a mean lifetime of 5 years. If you were in charge of quality control at the factory,...

Changes in Education Attainment: According to the U.S. Census Bureau, the distribution of Highest Education Attainment...

Changes in Education Attainment: According to the U.S. Census Bureau, the distribution of Highest Education Attainment in U.S. adults aged 25 - 34 in the year 2005 is given in the table below. Census: Highest Education Attainment - 2005 No High School Associate's Bachelor's Graduate or Diploma Diploma Degree Degree Professional Degree Percent 14% 48% 8% 22% 8% In a survey of 4000 adults aged 25 - 34 in the year 2013, the counts for these levels of educational attainment...