8 - STAT 3360 - FALL 2015 DUE BY NOVEMBER 3 SECTION [CIRCLE ONE! =>] FIRST NAME 001 002 LAST NAME 501 INFERENCES ABOUT THE POPULATION PLEASE, READ SECTIONS 10.2, 11.2, AND 12.1 - 12.2 TO SUCCEED ON THIS HOMEWORK AND ON THE FINAL EXAM. TABLES 4 AND 5 AND CLASS NOTES ARE REQUIRED. 1. [30 POINTS = 5 + 10 + 5 + 10] A SAMPLE OF 25 EMPLOYEES WAS DRAWN FOR THE ANALYSIS OF THE AVERAGE BONUS EARNED LAST YEAR. ASSUME THAT THE INDIVIDUAL BONUS IS NORMALLY DISTRIBUTED WITH UNKNOWN PARAMETERS. SAMPLE SUMMARIES: (SAMPLE MEAN) = $6,400 AND (SAMPLE STANDARD DEVIATION) = $1,200. (A) AT THE 1% SIGNIFICANCE LEVEL, DO WE HAVE SUFFICIENT EVIDENCE THAT THE POPULATION AVERAGE BONUS WAS BELOW $7,000? CIRCLE APPROPRIATE ANSWER: YES! NO! (B) SHOW THE TEST STATISTIC VALUE, THE CRITICAL VALUE(S) NEEDED FOR YOUR DECISION AND FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = CRITICAL VALUE(S): REJECTION RULE STATES... (C) AT THE SAME 1% SIGNIFICANCE LEVEL, DO WE HAVE SUFFICIENT EVIDENCE THAT THE POPULATION AVERAGE BONUS DIFFERS FROM $7,000? NO! CIRCLE APPROPRIATE ANSWER: YES! (D) SHOW THE CRITICAL VALUE(S) NEEDED FOR YOUR DECISION AND FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = CRITICAL VALUE(S): REJECTION RULE STATES... 1 HOMEWORK 8 - STAT 3360 - FALL 2015 DUE BY NOVEMBER 3 2. (A) [30 POINTS = 5+ 10 + 5 + 10] REPEAT THE PREVIOUS PART (WITH SAMPLE SIZE = 25) IF THE SUMMARIES (SAMPLE MEAN) = $6,400 AND (SAMPLE STANDARD DEVIATION) = $1,200 ARE DERIVED UNDER THE ASSUMPTION THAT THE POPULATION STANDARD DEVIATION IS KNOWN AS $1,250. WHAT IS THE TEST STATISTIC VALUE? TEST STATISTIC VALUE = (B) AT THE 1% SIGNIFICANCE LEVEL, DO WE HAVE SUFFICIENT EVIDENCE THAT THE POPULATION AVERAGE BONUS WAS BELOW $7,000? NO! CIRCLE APPROPRIATE ANSWER: YES! (C) SHOW THE CRITICAL VALUE(S) NEEDED FOR YOUR DECISION AND FORMULATE THE REJECTION RULE. CRITICAL VALUE(S): REJECTION RULE STATES... (D) AT THE SAME 1% SIGNIFICANCE LEVEL, DO WE HAVE SUFFICIENT EVIDENCE THAT THE POPULATION AVERAGE BONUS DIFFERS FROM $7,000? NO! CIRCLE APPROPRIATE ANSWER: YES! (E) SHOW THE CRITICAL VALUE(S) NEEDED FOR YOUR DECISION AND FORMULATE THE REJECTION RULE. CRITICAL VALUE(S): REJECTION RULE STATES... 2 HOMEWORK 8 - STAT 3360 - FALL 2015 DUE BY NOVEMBER 3 3. (A) (B) [40 POINTS = 5 + 10 + 5 + 10 + 10] A STUDY OF THE VARIANCE IN STUDENTS' MONTHLY EXPENSES WAS CONDUCTED. ASSUME THAT INDIVIDUAL MONTHLY EXPENSE FOR A RANDOMLY SELECTED STUDENT IS NORMALLY DISTRIBUTED. A SAMPLE OF 16 STUDENTS WAS SELECTED AND THE SAMPLE SUMMARIES WERE FOUND AS FOLLOWS: (SAMPLE MEAN) = $1,350 AND (SAMPLE STANDARD DEVIATION) = $12. AT THE 1% SIGNIFICANCE LEVEL, DO RESEARCHERS HAVE EVIDENCE THAT THE POPULATION VARIANCE WAS BELOW 400? NO! CIRCLE APPROPRIATE ANSWER: YES! SPECIFY THE TEST STATISTIC VALUE, CRITICAL VALUE, AND TEST STATISTIC VALUE. THEN FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = CRITICAL VALUE(S): REJECTION RULE STATES... (C) AT THE 1% SIGNIFICANCE LEVEL, CAN RESEARCHERS STATE THAT THE POPULATION VARIANCE WAS ABOVE 75? CIRCLE APPROPRIATE ANSWER: YES! NO! (D) SPECIFY THE TEST STATISTIC VALUE, CRITICAL VALUE, AND TEST STATISTIC VALUE. THEN FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = CRITICAL VALUE(S): REJECTION RULE STATES... (E) ESTIMATE THE POPULATION VARIANCE WITH THE 95% CONFIDENCE (ROUND ND OFF THE ANSWERS TO THE 2 DECIMAL PLACE). SPECIFY THE CRITICAL VALUES NEEDED FOR THIS PROCEDURE. UPPER CONFIDENCE LIMIT = CRITICAL VALUE = LOWER CONFIDENCE LIMIT = CRITICAL VALUE = PROBLEM 1 2 3 TOTAL 30 30 40 100 POINTS MAXIMUM 3