Question

Where do "A" students sit in the classroom? There are still 151 students enrolled in my four Statistics classes this semester, 45 of which currently have an A. I recorded where the A students are sitting and here are the results: 16 of the A students sit in or near the front, 19 sit in the middle, and 10 sit in or near the back. Is there sufficient evidence to support the claim that "A" students are not evenly distributed throughout the classroom? Use a .05 significance level.

1)Write the claim and opposite in symbolic form next to HO and H1.
2)Draw a Chi-square curve, Find the critical value and shade the critical region
3)Find the test statistic and its p-value
4)Write the final conclusion

Ho:
H1:
Critical Value:
Test Statistic:
P-Value:
Conclusion:

Answer 1

1)

Ho: "A" students are evenly distributed throughout the classroom [Opposite]

H1: "A" students are not evenly distributed throughout the classroom [Claim]

2)

level of significance, α=   0.05              
Degree of freedom=k-1=   3   -   1   =   2

Critical value = 5.9915 [ Excel function: =chisq.inv.rt(α,df) ]

3)

Chi square test for Goodness of fit  
total frequency=   45
expected frequncy,E = expected proportions*total frequency =1/3*45=15

observed frequencey, O	expected proportion	expected frequency,E	(O-E)	(O-E)²	(O-E)²/E
16	0.3333	15.000	1.00	1.00	0.067
19	0.3333	15.000	4.00	16.00	1.067
10	0.3333	15.000	-5.00	25.00	1.667

chi square test statistic,X² = Σ(O-E)²/E =   2.8000
  

Degree of freedom=k-1=   3   -   1   =   2
                  
P value =   0.2466   [ excel function: =chisq.dist.rt(test-stat,df) ]          

4)

conclusion:Decision: P value >α , Do not reject Ho

there is not sufficient evidence to support the claim that "A" students are not evenly distributed throughout the classroom