Question

This question has 7 parts. Each of the 7 parts (Part A - Part G) has a dropdown list of possible answers. Choose the best answer from the dropdown list for EACH part of the question below.

Your analysis will focus on the variables "Current residence" and "Gender"

Researchers are interesting in examining if there is an association between a person's gender and their current residence type, conduct a two variable chi-square test to test whether there appears to be any association between gender and current residence type, using an alpha level (α) of 0.01. Provide the following information:

You will use the information above to complete the question parts below.

Part A: Which of the following represents the appropriate null hypothesis(H₀), given this research question of interest?

PART A ANSWER: H₀:                            [ Select ]                       ["μ of current residence type = μ of gender", "Gender and current residence type are independent", "μ of current residence type - μ of gender=0", "Gender and current residence type are related", "Gender and current residence type are quantitative"]      

Part B: Which of the following represents the appropriate alternative hypothesis (H₁), given this research question of interest?

PART B ANSWER: H₁:                            [ Select ]                       ["μ of current residence type ≠ μ of gender", "Gender and current residence type are qualitative", "μ of current residence type - μ of gender ≠ 0", "H0 is false", "Gender and current residence are the same variable"]      

Part C: What is your degrees of freedom?

PART C ANSWER:                            [ Select ]                       ["14", "0.068", "5", "2", "46"]      

Part D: What is your calculated chi-square statistic?

PART D ANSWER:                            [ Select ]                       ["1.297", "0.068", "5", "3574.723", "10.255"]      

Part E: What is the p-value associated with your test statistic?

PART E ANSWER:                             [ Select ]                       ["0.583", "0.068", "0.000", "0.246", "10.255"]      

Part F: What is your decision about the null hypothesis based on your test results?

PART F ANSWER:                             [ Select ]                       ["Reject the null", "Fail to reject (i.e., retain) the null"]      

Part G: The best interpretation of the appropriate decision regarding the null hypothesis would be: "Based on our study, we                           [ Select ]                       ["have", "do NOT have"]         enough evidence to conclude that there appears to be an association between gender and current residence type".

Answer 1

This is a simple question regarding the generation and interpretation of the chi square test and its inference.

However before proceeding with the solution ot the question ,it has to be noted that the original dataset of the contigency table is NOT attached with the problem. It required reference from internet support to get the relevant data attached with this problem.

We inferred from the online help that

Now let us proceed with the hypothesis test and its inferences drawn using the chi square test .

a). Let us build the hypothesis test.

Before that we need to identify the variables to check the hypothesis on .

Clearly the variables are Residence type and Gender

We need to check if gender plays a role in choice of residence type.

Thus,

A.Hence for first question we should go with the option having

"Gender and current residence type are independent"

B.For second question we should go with the option

Ho is false / the two variables are not independent. They are dependent.

C. The degree of freedom as indicated above is equal to 5.

D. The chi square is 10.255

E. Let us refer ot the chi square ptable for degree of freedom 5, chi square value of 10.255 and confidence level of 0.01.

We observe that it is equal to 0.068

Hence the p value of the experiment /observational study is 0.068

F. The p value of the experiment is >0.01 which is our critical limit /cut off limit.

The result is not significant at p < .01.

Hence we have to reject the null hypothesis that the variables (residence type and gender) are independent.

G. In other words,They are dependent on each other.

"Based on our study, we have enough evidence to conclude that there appears to be an association between gender and current residence type"