10 - STAT 3360 - SPRING 2016 DUE BY APRIL 19 [SECTIONS 002, 003] || BY APRIL 20 [SECTION 001] SECTION [CIRCLE ONE! =>] FIRST NAME 001 002 LAST NAME 003 READ SECTIONS 15.1 AND 15.2. TABLE 5 IS REQUIRED. PROBLEM 1 [SECTION 15.1] EDUCATION EXPERTS BELIEVE THAT THE GRADE DISTRIBUTION AMONG STUDENTS WHO TAKE MATH OR STAT UNDERGRADUATE COURSES SHOULD BE AS SHOWN BELOW. THE STUDY OF 400 STUDENTS HAS SHOWN THE COUNTS SHOWN IN THE LAST ROW (COUNTS). GRADE PROPORTION OBSERVED A B C D F W TOTAL 15% 20% 40% 10% 10% 5% 100% 66 84 148 48 46 8 400 EXPECTED [A] WHAT ARE THE EXPECTED COUNTS IN EACH CATEGORY? SHOW THEM IN THE TABLE ABOVE. [B] WHAT IS THE TEST STATISTIC VALUE? TEST STATISTIC VALUE = HOW MANY DEGREES OF FREEDOM WILL YOU ASSESS? NUMBER OF DEGREES OF FREEDOM = [C] AT THE 5% SIGNIFICANCE LEVEL, DO THE RECORDS PROVIDE EVIDENCE THAT THE GRADE DISTRIBUTION MAY DIFFER FROM THE EXPECTATIONS EXPRESSED BY EXPERTS? CIRCLE YES (IF REJECT) OR NO (IF DO NOT REJECT) HERE. WHAT IS THE CRITICAL VALUE? STATE THE REJECTION RULE. REJECT THE NULL HYPOTHESIS IF [D] AT THE 1% SIGNIFICANCE LEVEL, DO THE RECORDS PROVIDE EVIDENCE THAT THE GRADE DISTRIBUTION MAY DIFFER FROM THE EXPECTATIONS EXPRESSED BY EXPERTS? CIRCLE YES (IF REJECT) OR NO (IF DO NOT REJECT) HERE. WHAT IS THE CRITICAL VALUE? STATE THE REJECTION RULE. REJECT THE NULL HYPOTHESIS IF 1 HOMEWORK 10 - STAT 3360 - SPRING 2016 DUE BY APRIL 19 [SECTIONS 002, 003] || BY APRIL 20 [SECTION 001] PROBLEM 2 [SECTION 15.2] STATISTICAL STUDIES WERE CONDUCTED AMONG STUDENTS. THE PURPOSE WAS TO FIND OUT WHETHER PERFORMANCE EVALUATIONS FOR INSTRUCTORS TEACHING DIFFERENT SUBJECT AREAS WERE DISTRIBUTED HOMOGENEOUSLY. THE TABLE BELOW SHOWS THE TOTALS ONLY. THE CATEGORIES LISTED BELOW INCLUDE (EX = EXCELLENT), (VG = VERY GOOD), GOOD, FAIR, POOR, AND (VP = VERY POOR). SUPPOSE THE CHI-SQUARE HOMOGENEITY TEST HAS SHOWN THE VALUE OF TEST STATISTIC = 29.875. COURSE EX SATISFACTION LEVEL VG GOOD FAIR POOR VP TOTAL MATH 400 STAT 300 PHYSICS 200 CHEMISTRY 100 TOTAL 300 200 200 150 100 50 1,000 [A] FIND THE EXPECTED COUNTS. FILL THE CELLS IN THE TABLE ABOVE. [B] HOW MANY DEGREES OF FREEDOM WILL BE ASSESSED TO THE CHI-SQUARED STATISTIC USED FOR THE HOMOGENEITY TEST? NUMBER OF DEGREES OF FREEDOM = [C] AT THE 1% SIGNIFICANCE LEVEL, DO YOU HAVE EVIDENCE THAT THE EVALUATION VARIES FROM ONE SUBJECT AREA TO THE OTHER? CIRCLE YES (IF REJECT) OR NO (IF DO NOT REJECT) HERE. WHAT IS THE CRITICAL VALUE? STATE THE REJECTION RULE. REJECT THE NULL HYPOTHESIS IF [D] AT THE 5% SIGNIFICANCE LEVEL, DO YOU HAVE EVIDENCE THAT THE EVALUATION VARIES FROM ONE SUBJECT AREA TO THE OTHER? CIRCLE YES (IF REJECT) OR NO (IF DO NOT REJECT) HERE. WHAT IS THE CRITICAL VALUE? STATE THE REJECTION RULE. REJECT THE NULL HYPOTHESIS IF 2