Question

In: Statistics and Probability

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.

Solutions

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 Ei=row total*column 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 =(Oi-Ei)2/Ei 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


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