A study was performed to examine the personal goals of children in grades 4, 5, and...

A study was performed to examine the personal goals of children in grades 4, 5, and 6. A random sample of students was selected from each of the grades 4, 5, and 6 from schools in Georgia. The students received a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Results are presented by the gender of the child in the table below:

Gender
Goal	Boys	Girls
Make good grades	96	295
Be popular	32	45
Be good in sports	94	40

a) What would be the null hypothesis for a chi-square test based on these data?

b) What is the value of the chi-square statistic based on the data presented in this table?

c) Are the data statistically significant at the 5% significance level?

Could I please get details step solutions please. I have no clue how to do it. Thank you.

Expert Solution

a)Null hypothesis:HO: Gender and type of goals are independent to each other

b)applying chi square test:

Observed	Oi	Boys	Girls	Total
	Make good grades	96	295	391
	BE popular	32	45	77
	Be good in sports	94	40	134
	total	222	380	602

Expected	E_i=row totalcolumn total/grand total*	Boys	Girls	Total
	Make good grades	144.19	246.81	391
	BE popular	28.40	48.60	77
	Be good in sports	49.42	84.58	134
	total	222	380	602

chi square χ²	=(O_i-E_i)²/E_i	Boys	Girls	Total
	Make good grades	16.1053	9.4089	25.514
	BE popular	0.4576	0.2673	0.725
	Be good in sports	40.2264	23.5007	63.727
	total	56.789	33.177	89.966

from above Chi square test statistic =89.966

c)

degree of freedom(df) =(rows-1)*(columns-1)=

2

for 2 df and 0.05 level of signifcance critical region χ2=

5.991

as test statisitc 89.966 is higher then critical value we reject null hypotheis

we have sufficient evidence to conclude that Gender and type of goals are dependent to each other

orchestra answered 1 year ago

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