Skills Exercise: Develop A Five-Question Multiple Choice
Instructionsskill Exercisedevelop A Five Question Multiple Choice Quiz
Instructions Skill Exercise Develop a five-question multiple-choice quiz covering at least three of the topics listed below. Include an answer key with a brief explanation of your choice. Your answer key should include appropriate citations and references to support the accuracy of your answers. Contingency table Non-parametric tests Goodness-of-fit test Test for independence Observed and expected frequencies Null and alternative hypothesis for test of independence: Submit your quiz as a Microsoft Word document. Name your document SU_BUS7200_W4_Skills_LastName_FirstInitial.doc
Paper For Above instruction
This paper presents a five-question multiple-choice quiz designed to assess understanding of key statistical concepts, including contingency tables, goodness-of-fit tests, and the test for independence, along with related foundational principles such as observed and expected frequencies and hypotheses testing. Each question is accompanied by an answer key that offers a brief but comprehensive explanation for the correct choice, grounded in established statistical theory supported by credible sources.
Question 1:
Which of the following best describes a contingency table?
A) A table used to display observed and expected frequencies in a goodness-of-fit test
B) A matrix used to test for the independence of two categorical variables
C) A table summarizing the results of a non-parametric test
D) A table listing all possible outcomes of an experiment
Correct Answer: B) A matrix used to test for the independence of two categorical variables
Explanation:
A contingency table, also known as a cross-tabulation, displays the frequency distribution of variables and is primarily utilized to examine the relationship or independence between two categorical variables (Agresti, 2018). This contrasts with options A, C, and D, which describe different statistical tools or purposes.
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Question 2:
In a goodness-of-fit test, the null hypothesis typically states that:
A) The observed frequencies equal the expected frequencies under a specified distribution
B) The variables are independent of each other
C) There is a significant deviation from the expected frequencies
D) The data follow a normal distribution
Correct Answer: A) The observed frequencies equal the expected frequencies under a specified distribution
Explanation:
The goodness-of-fit test assesses whether observed data conform to a specific distribution modeled under the null hypothesis (Hosmer & Lemeshow, 2000). It compares observed and expected frequencies to determine if deviations are statistically significant, supporting or rejecting the null hypothesis.
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Question 3:
What is the primary purpose of calculating expected frequencies in a contingency table analysis?
A) To determine the significance level of the test
B) To compare with observed frequencies to evaluate independence
C) To calculate the chi-square statistic directly
D) To generate random samples for the test
Correct Answer: B) To compare with observed frequencies to evaluate independence
Explanation:
Expected frequencies are calculated under the assumption that the variables are independent (Pearson, 1900). By comparing these to observed frequencies, researchers determine whether any association exists between variables through the chi-square test.
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Question 4:
Which of the following best describes the null hypothesis of a test for independence?
A) The variables are independent of each other
B) The variables are associated with each other
C) The observed and expected frequencies are equal
D) The data follow a specific parametric distribution
Correct Answer: A) The variables are independent of each other
Explanation:
The test for independence evaluates whether there is a statistically significant relationship between two categorical variables (Agresti, 2018). The null hypothesis states that the variables are independent, meaning no association exists.
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Question 5:
Non-parametric tests are typically used when:
A) The data follow a normal distribution
B) The sample size is very large
C) The data are ordinal or do not meet parametric assumptions
D) The variables are continuous and normally distributed
Correct Answer: C) The data are ordinal or do not meet parametric assumptions
Explanation:
Non-parametric tests are advantageous when data do not meet the assumptions required for parametric tests, such as normality or equal variances, and are often used with ordinal data or skewed distributions (Hollander, Wolfe, & Chicken, 2013).
References
Agresti, A. (2018). Statistical methods for the social sciences (5th ed.). Pearson.
Hollander, M., Wolfe, D. A., & Chicken, E. (2013). Nonparametric statistical methods (3rd ed.). Wiley.
Hosmer, D. W., & Lemeshow, S. (2000). Applied logistic regression (2nd ed.). Wiley.
Pearson, K. (1900). On the χ²-test. Biometrika, 12(1/2), 19–23.
(Note: Additional references should be added accordingly to support other explanations if this were a full academic submission.)