Question

A study was conducted to explore the relationship between a child's birth order and the chances of becoming a juvenile delinquent. The participants were a random sample of girls enrolled in public high schools in a large city. Each girl filled out a questionnaire that asked for their birth order and measured whether they had shown delinquent behavior. The data are given in the table below. Test at the 0.01 significance level.

Yes No

Oldest 24 285

In-Between 29 247

Youngest 35 211

Only child 23 70

SHOW STEP BY STEP

A) Calculate all the expected values

B)Calculate the contributions to the chi-squared statistic, label which each is

C) Which cell will contribute the most to the chi-squared statistic

D) Which cell will contribute the least to the chi-squared statistic

E)Calculated the chi-squared statistic

Answer 1

Given,

	Yes	No	Total
Oldest	24	285	309
In-between	29	247	276
Youngest	35	211	246
Only child	23	70	93
Total	111	813	924

A)

E: Expected Value

	Yes	No	Total
Oldest	(309*111)/924	(309*813)/924	309
In-between	(276*111)/924	(276*813)/924	276
Youngest	(246*111)/924	(246*813)/924	246
Only child	(93*111)/924	(93*813)/924	93
Total	111	813	924

	Yes	No	Total
Oldest	37.1201	271.8799	309
In-between	33.1558	242.8442	276
Youngest	29.5519	216.4481	246
Only child	11.1721	81.8279	93
Total	111	813	924

Test Statistic

O-E		Yes	No
	Oldest	-13.1201	13.1201
	In-between	-4.1558	4.1558
	Youngest	5.4481	-5.4481
	Only child	11.8279	-11.8279

contributions to the chi-squared statistic:

(O-E)/E2	Yes	No
Oldest	4.637317	0.633139
In-between	0.520905	0.07112
Youngest	1.004376	0.137129
Only child	12.52227	1.709682

C)

Cell contribute the most to the chi-squared statistic : Only child - Yes : 12.52227

D)

Cell contribute the least to the chi-squared statistic : In-between - no : 0.07112

E)

Chi-squared statistic:

(O-E)2/E		Yes	No	Total
	Oldest	4.637317	0.633139	5.270456
	In-between	0.520905	0.07112	0.592025
	Youngest	1.004376	0.137129	1.141505
	Only child	12.52227	1.709682	14.23195
	Total			21.23593

Chi-squared statistic:

Chi-squared statistic: 21.23593