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 1 year ago

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