Chi-Square Test Questions: Expert Solutions

How does the size of the cross-tabulation table impact the chi-square value.

Chi-Square tests are nonparametric tests. Discuss the following:
What are the differences between parametric tests and nonparametric tests?
What are the requirements for Chi-Square tests?
What are the limitations of Chi-Square tests?

Chi-square tests are nonparametric tests that examine nominal categories as opposed to numerical values. Consider a situation in which you may want to transform numerical scores into categories. Provide a specific example of a situation in which categories are more informative than the actual values.

For this study, why we would want to use Chi-Squared?
1.A study investigating the effects of second-hand smoke in working environments asked the following question: “How often do you experience second-hand smoke in a work environment/function? Never, Occasionally, Fairly Often, Very Often, Almost Always.” The question was asked of managers and employees to determine whether there was an association between position and the amount of second-hand smoke exposure.

Explain what changes would be required so that you could analyze the hypothesis using a chi-square test. For instance, rather than looking at test scores as a range from 0 to 100, you could change the variable to low, medium, or high. What advantages and disadvantages do you see in using this approach? Which is the better option for this hypothesis, the parametric approach or nonparametric approach?

A chi-square value of 6.15 is calculated from data in a $4x5$ contingency table. Assuming $\alpha =0.05$, identify the critical value.
26.217
31.410
21.026
16.919

You want to know whether people in different regions of the country are equally likely to vote Sarah Duterte, Peter Cayetano, Mar Roxas, or any candidate other than the three in the next election. You would use
A. chi-square test of independence.
B. either chi-square test (goodness-of-fit or test of independence), depending on how you set up the problem.
C. chi-square goodness-of-fit test.
D. both chi-square tests, in order to check the results of one with the other.

Compare the chi-square p-value and Fisher's exact test p-value and determine which is more accurate.

Explain why the chi-square is called a goodness-of-fit test.

Distinguish the difference (purpose) between the two different types of chi-square
1.Chi-square test for independence (CTI)
2.Chi-square test for goodness of fit (CGF)
3.What type of variables are we using for a chi-square?

Choose an appropriate test from the list of five tests for the given case.

Find the pattern of the data of Chi-square goodness-of-fit from two options.

A) Explain why the chi-square goodness-of-fit test is not an appropriate way to find out.
B) What might you do instead of weighing the nuts in order to use a x2 test?
Nuts A company says its premium mixture of nuts con- tains 10% Brazil nuts, 20% cashews, 20% almonds, and 10% hazelnuts, and the rest are peanuts. You buy a large can and separate the various kinds of nuts. Upon weigh- ing them, you find there are 112 grams of Brazil nuts, 183 grams of cashews, 207 grams of almonds, 71 grams of hazelnuts, and 446 grams of peanuts. You wonder whether your mix is significantly different from what the company advertises.

A chi-square homogeneity test is to be conducted to decide whether four populations are nonhomogeneous with respect to a variable that has eight possible values. What are the degrees of freedom for the ${\displaystyle x^2}$-statistic?