Question

The Chi-squared test has been used earlier to test a hypothesis about a population variance. It is also a hypothesis testing procedure for when one or more variables in the research are categorical (nominal).

Chi-squared Goodness of Fit Test

Chi-squared Test for Independency

Question 1. Describe an example of a research question where a Chi-squared test has been used. Mention the two hypotheses of the problem and display a numerical demonstration of your example. In particular, interpret the test P value in the context of your research example.

Question 2. Describe why the Chi-squared tests of the types mentioned above are always right-tailed hypothesis testing problems.

Anyone help please.......

Answer 1

1) Suppose two samples of votes for two candidates A and B for a public office are taken,one from among the residents of rural areas. The results are given in the adjoining table. We need to examine whether the nature of the area is realated to voting preferance in this election?

AREA	A	B	TOTAL
RURAL	620	380	1000
URBAN	550	450	1000
TOTAL	1170	830	2000

NULL HPOTHESIS H0: The nature of the area is independent of the voting preference in the election.

ALTERNATIVE HYPOTHESIS Ha : The nature of the area is NOT independent of the voting preference in the election.

Now we will calculate expected frequencies

E(620)= 1170X1000/2000= 585

E(380)= 830X1000/2000= 415

E(550)= 1170X1000/2000= 585

E(450)= 830X1000/2000= 415

Degrees of freedom= (2-1)*(2-1)= 1

alpha= 0.05 (Assumed)

The P-Value is 0.001492

Since P value is SMALLER than 0.05 level of significance hence significant.

Conclusion: Since P value is significant we therefore reject null hypothesis and conclude that we have sufficient evidence to show that the nature of the area is NOT independent of the voting preference in the election.

2) Because in both test we used test statistic the actual difference between the 'observed' and 'expected' values, that quantity is squared, meaning that whether the observed is more or less than the expected, the result is always a positive measure, therefore it is always right-tailed distribution.

NOTE: Answer is best to my knowledge. You can do more research for question 2 if you want. I hope it will help you. Thank you :)