In: Statistics and Probability
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.
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