Question 5 2 pts A university is considering implementing of the following three grading systems: 1) All grades are pass-fail 2) All grades are on the 4.0 system 3) 90% of the grades are on the 4.0 system and 10% are pass-fail. A survey is taken to determine whether there is a relationship between undergraduate major and grading system preference. A random sample of 200 students with fine arts majors is selected. Each student is asked which of the three grading system he or she prefers. The results are shown in the following 3x3 contingency table: Pass-fail 4.0 and pass-fail 4.0 (totals) Fine arts 26 55 19 100 Arts and Science 24 118 58 200 Engineering 20 112 68 200 (totals) 70 285 145 500 Chi-Square test (Bonus in RED): 1. What is the independent and the dependent variable? 2. What is the null hypothesis? 3. What is the test result? (Possible bonus points when you complete the test) 4. Will you reject of fail to reject the null based on the test result.
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A University is considering changing its grading system. The three grading systems under consideration are: 1) All grades are Pass/Fail, 2) All grades are on the 4.0 system, and 3) 80% of the grades are on the 4.0 system, and 20% of the grades are Pass/Fail. A survey is taken to determine if there is a relationship between undergraduate major and grading system preference. A random sample of math and psych majors is taken, and each student is asked to state their grading system preference. The results are shown below. Do math and psych majors differ in their grading system preferences? Use Chi-square test with a significance level of α = .05 Grading System: Pass/Fail Only; 80% 4.0 System / 20% Pass/Fail; 4.0 System Only Undergraduate Major: Psych: n=80, n=90, n=120 Math: n=100, n=50, n=20
Adi S.
Problem 1: [20 points = 5 + 5 + 5 + 5] A two-by-two contingency table contains summaries obtained from n = 250 students. Two binary variables, X and Y were processed, where X takes values "In Class" or "Online" and Y identifies blood pressure as "Pass" or "Fail". The summaries are presented below: Pass Fail Row Sum In Class 88 12 100 Online 112 38 150 Column Sum 200 50 250 1. Estimate expected counts and show them in the table similar to observed frequencies. 2. Evaluate the x2-test statistic for independence between X and Y. 3. At significance level ̑ = 0.05, do you have sufficient evidence that class modality and pass-fail may be viewed as dependent variables? 4. At significance level ̑ = 0.01, do you have sufficient evidence that class modality and pass-fail may be viewed as dependent variables? Show critical values for each case and formulate rejection rule. Solution
Q2) Chi-Square Test for Goodness of Fit (11 points) A psychology professor was interested in providing assessment options for students in her Memory and Cognition course. She offered students the following three options for a final assessment in the course: 1) A 50-point multiple-choice exam, 2) A five-page essay, 3) A 15 minute in-class presentation. The professor was curious if the choices would be evenly distributed or if there would be a significant difference in final selection distribution. Here are the numbers of students who selected each type of assessment: Multiple-choice exam = 38, Essay = 13, In-class presentation = 9. Conduct a Chi-square test for goodness of fit with an alpha level of .05 to answer this research question. a) What is the variable in this test? What type of variable is it (nominal, ordinal, or continuous)? (2 points total, 1 for each answer) b) State the null and alternative hypotheses in words (2 points total: 1 for each hypothesis) c) Calculate X² statistic (3 points total: 1 for final answer, 1 for setting up the correct OFs and EFs, 1 for correct calculation process) d) Calculate the degrees of freedom and then identify the critical value (2 points total, 1 for df, 1 for critical value) e) Compare the X² statistic with the critical value, then report the hypothesis test result, using "reject" or "fail to reject" the null hypothesis in the answer (1 point total, .5 for each answer) f) Explain the conclusion in a sentence or two (1 point)
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