Question

In: Statistics and Probability

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, etc.) 15% 75

Using a significance level of 0.05, test the claim that the Aurora distribution fits the distribution obtained by the census personnel.

Expert Solution

null hypothesis:Ho: Aurora distribution fits the distribution obtained by the census personnel.

alternate hypothesis:Ha: Aurora distribution is different thn the distribution obtained by the census personnel.

degree of freedom =categories-1=6-1=5

for 5 df and 0.05 level rejection region >11.070

applying chi square goodness of fit test:

		observed	Expected	Chi square
category	Probability(p)	O_i	E_i=total*p	R²_i=(O_i-E_i)²/E_i
married w children	0.250	95.000	125.00	7.200
married w no children	0.200	110.000	100.00	1.000
single parent	0.050	35.000	25.00	4.000
single individual	0.150	65.000	75.00	1.33
one person	0.200	120.000	100.00	4.00
other	0.150	75.000	75.00	0.00
total	1.000	500	500	17.53

as test statistic 17.53 is higher than critical value ; we reject null hypothesis

we have sufficient evidence to conclude that Aurora distribution is different from the distribution obtained by the census personnel.

orchestra answered 2 years ago

10.The distribution of vehicles sales in the United States in the year 2000 was the following:...

10.The distribution of vehicles sales in the United States in the year 2000 was the following: Type of car Small Midsize Large Luxury % 32.8 44.8 9.4 3.0 A simple random sample of 500 vehicles sales was taken this year and the Distribution is as follow: Type of car Small Midsize Large Luxury % 133 249 47 71 At the 5% significant level, do the data provides sufficient evidence to conclude that the distribution of vehicle sales this year has...

According to the 1980 Census, the United States population was approximately 226,540,000 in 1980, and according...

According to the 1980 Census, the United States population was approximately 226,540,000 in 1980, and according to US Census Bureau estimates, approximately 317,300,000 at the beginning of 2014. Using Census data for 1980 and estimates derived from mortality data and census estimates for 2014, we arrive at the population estimates given in the table below: Year Total Population Ages 15–24 Ages 25–44 Ages 45–64 1980 226,540,000 42,475,000 62,707,000 44,497,000 2014 317,300,000 43,956,000 84,410,000 83,747,000 The National Center for Health Statistics...

According to the U.S. Census Bureau, 11% of children in the United States lived with at...

According to the U.S. Census Bureau, 11% of children in the United States lived with at least one grandparent in 2009 (USA TODAY, June 30, 2011). Suppose that in a recent sample of 1570 children, 224 were found to be living with at least one grandparent. At a 5% significance level, can you conclude that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%? Use both the p-value...

According to the US Census Bureau, the Gini Coefficient in the United States was 0.397 in...

According to the US Census Bureau, the Gini Coefficient in the United States was 0.397 in 1967, and 0.480 in 2014. The Gini coefficient is a measure of inequality that ranges from 0 to 1, where higher numbers indicate greater inequality. According to the World Bank, countries with Gini coefficients between 0.5 and 0.7 are characterized as highly unequal. Using the idea that Incentives Matter, analyze BOTH the pros of some income inequality and the cons of excessive income inequality....

A) According to the National Institute of Health, 34% of adults in the United States are...

A) According to the National Institute of Health, 34% of adults in the United States are overweight. Suppose we sample 20 adults. Let X denote the number of overweight people among them. What is the probability that more than 6 of the adults will be overweight? Round to four decimal places. B) According to the National Institute of Health, 34% of adults in the United States are overweight. Suppose we sample 20 adults. Let X denote the number of overweight...

s According to the 2010 Census, 12.8% of all housing units in the United States were...

s According to the 2010 Census, 12.8% of all housing units in the United States were vacant. A county supervisor wonders if her county is different from this. She randomly selects 180 housing units in her county and finds that 36 of the housing units are vacant. A) state the hypothesis B) check the appropriate conditions for a hypothesis C) calculate the test statistic and the p value D) state your conclusion using 0.05 as threshold value fot comparing p-value

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...

The weights of newborn children in the United States vary according to the Normal distribution with...

The weights of newborn children in the United States vary according to the Normal distribution with mean 7.5 pounds and standard deviation 1.25 pounds. The government classifies a newborn as having low birth weight if the weight is less than 5.5 pounds. A study of learning in early childhood chooses an SRS of 3 children. 1. Is it okay to use normal calculations for this problem? Explain 2. Describe the sampling distribution. 3. What is the probability that the mean...

In the United States, according to a 2018 review of National Center for Health Statistics information,...

In the United States, according to a 2018 review of National Center for Health Statistics information, the average age of a mother when her first child is born in the U.S. is 26 years old. A curious student at CBC has a hypothesis that among mothers at community colleges, their average age when their first child was born is lower than the national average. To test her hypothesis, she plans to collect a random sample of CBC students who are...

According to a national census for a particular country, the proportion of families with three or...

According to a national census for a particular country, the proportion of families with three or more children (aged less than 25) declined from 3939% in 1961 to 1919% in 2011. Suppose we estimate that this proportion is 17.617.6% this year. In order to market products to large families, we randomly select 25002500 families in this nation for a survey. Complete parts (a) through (d) below. b) In our sample, we find 19.119.1% of the families have three or more...