Question

A social survey was administered to a sample of adults. A subsample of these adults, selected randomly, appears in the table below. Each respondent has been classified as either a city dweller, a suburbanite, or a rural dweller. Are there statistically significant differences by place of residence for the number of

children living in these households (at an alpha level of 0.05)? Make sure to

round to four digits for each step and your final answer.

Number of Children Urban Suburban Rural

1 0 1

1 1 4

0 0 2

2 0 3

1 2 3

0 2 2

2 3 5

2 2 0

1 2 4

0 1 6

Answer 1

ANSWER:

Here we need to use one way ANOVA.

Hypotheses are:

H0: There is no difference by place of residence in the number of children in each household.

Ha: There is a difference by place of residence in the number of children in each household.

Following is the output of one way ANOVA:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Urban	10	10	1	0.66666667
Suburban	10	13	1.3	1.12222222
Rural	10	30	3	3.33333333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	23.26667	2	11.63333	6.81344902	0.004021854	3.354131
Within Groups	46.1	27	1.707407
Total	69.36667	29

The F test statistics is

F = 6.813

The p-value is:

p-value = 0.0040

Since p-value is less than 0.05 so we reject the null hypothesis.

That is we can conclude that there is a difference by place of residence in the number of children in each household.

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