Question

Answer True or False for the following:

1. Chi-square requires assumptions about the shape of the population distribution from which a sample is drawn.

2. Goodness of fit refers to how close the observed data are to those predicted from a hypothesis.

3. The null hypothesis (H0) states that no association exists between the two cross-tabulated variables in the population, and therefore the variables are statistically independent.

4. High chi square values indicate a high probability that the observed deviations are due to random chance alone

5. A scatter plot shows the direction of a relationship between the variables.

Answer 1

1. As Chi-Square test is an inferential statistics technique designed to test for significant relationships between two variables organized in a bivariate table, hence it requires no assumptions about the shape of the population distribution from which a sample is drawn. Hence the answer is FALSE

2. Goodness of fit refers to how close the observed data are to those predicted from a hypothesis - The formula for goodness of fit test is

Here Oj is the observed entity and Ej is the expected entity. This measures the closeness of the observed value with the predicted ones. Hence the answer is TRUE

3.  The null hypothesis (H0) states that no association exists between the two cross-tabulated variables in the population, and therefore the variables are statistically independent. In the case of the testing within two cross-tabulated variables in the population, the null hypothesis is whether the variables are mutually independent or not, hence we test the Chi-square test of independence. It actually determines the following thing: the absence of association between two cross-tabulated variables. The percentage distributions of the dependent variable within each category of the independent variable are identical. Hence the answer is TRUE

4. As Chi-square test determines whether the null hypothesis: the cross-tabulated variables are statistically independent or not. Chi-square test with p-value < 0.05 signifies that the null hypothesis is rejected at 5% level of significance. Hence high chi-square value indicates indicate a low probability that the observed deviations are due to random chance alone. Hence the answer is FALSE

5. Scatter Plot gives the relationship of two variables. Scatter plot gives the idea about how the variables are related to each other. if for the greater value of X gives a greater value of Y variable, then the scatter plot will show a linear trend between the two variables. Hence, the scatter plot shows the direction of a relationship between the variables. Hence the answer is TRUE

Thanks!!