9 - STAT 3360 - FALL 2015 DUE BY NOVEMBER 10 SECTION [CIRCLE ONE! =>] FIRST NAME 001 002 LAST NAME 501 INFERENCES ABOUT THE POPULATION PLEASE, READ SECTIONS 10.2, 10.3, 11.2, AND 12.1 - 12.3 TO SUCCEED ON THIS HOMEWORK AND ON THE FINAL EXAM. TABLES 4 AND 5 AND CLASS NOTES ARE REQUIRED. FIRST TWO PROBLEMS ARE FOCUSED ON INFERENCES ABOUT THE POPULATION MEAN AND POPULATION VARIANCE. MAKE SURE YOU KNOW WHICH TABLE IS TO BE USED! 1. (A) [20 POINTS = 10 + 10] A SAMPLE OF 16 CAR POLICIES WAS DRAWN FOR THE ANALYSIS OF CAR PREMIUM DISTRIBUTION. ASSUME THAT AN INDIVIDUAL PREMIUM IS NORMALLY DISTRIBUTED WITH UNKNOWN PARAMETERS. SAMPLE SUMMARIES ARE: (SAMPLE MEAN) = $96 AND (SAMPLE STANDARD DEVIATION) = $20. AT THE 1% SIGNIFICANCE LEVEL, IS THERE SUFFICIENT EVIDENCE THAT THE POPULATION AVERAGE PREMIUM WAS BELOW $110? CIRCLE APPROPRIATE ANSWER: YES! OR NO! 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... (B) AT THE 1% SIGNIFICANCE LEVEL, IS THERE SUFFICIENT EVIDENCE THAT THE POPULATION AVERAGE PREMIUM WAS ABOVE $85? CIRCLE APPROPRIATE ANSWER: YES! OR NO! 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 9 - STAT 3360 - FALL 2015 DUE BY NOVEMBER 10 2. (A) [20 POINTS = 10 + 10] A SAMPLE OF 16 CAR POLICIES WAS DRAWN FOR THE ANALYSIS OF CAR PREMIUM DISTRIBUTION. ASSUME THAT AN INDIVIDUAL PREMIUM IS NORMALLY DISTRIBUTED WITH UNKNOWN PARAMETERS. SAMPLE SUMMARIES ARE: (SAMPLE MEAN) = $96 AND (SAMPLE STANDARD DEVIATION) = $20. AT THE 5% SIGNIFICANCE LEVEL, IS THERE SUFFICIENT EVIDENCE THAT THE POPULATION VARIANCE FOR A CAR POLICIY PREMIUM WAS BELOW 960? CIRCLE APPROPRIATE ANSWER: YES! OR NO! 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... (B) AT THE 5% SIGNIFICANCE LEVEL, IS THERE SUFFICIENT EVIDENCE THAT THE POPULATION VARIANCE FOR A CAR POLICIY PREMIUM WAS ABOVE 250? CIRCLE APPROPRIATE ANSWER: YES! OR NO! SHOW THE CRITICAL VALUE(S) NEEDED FOR YOUR DECISION AND FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = CRITICAL VALUE(S): REJECTION RULE STATES... 2 HOMEWORK 9 - STAT 3360 - FALL 2015 DUE BY NOVEMBER 10 3. (A) [30 POINTS = 10 + 10 + 10] BUREAU OF LABOR STATISTICS CONDUCTED RESEARCH AIMED AT DRAWING CONCLUSIONS ABOUT THE AVERAGE SALARY CHANGE AMONG SOME CATEGORIES OF WORKERS. A SAMPLE OF 25 TECHICIANS WAS SELECTED AT RANDOM AND ANNUAL SALARY RECORDS WERE COLLECTED FOR TWO CONSECUTIVE YEARS (2012 AND 2013). THE SUMMARIES WERE FOUND AS FOLLOWS: (2012 SAMPLE MEAN) = $41,350 AND (2013 SAMPLE MEAN) = $45,358. ALSO THE SAMPLE STANDARD DEVIATION FOR INDIVIDUAL DIFFERENCES, D = (2013 SALARY) - (2012 SALARY), WAS FOUND AS $8,000. AT THE 1% SIGNIFICANCE LEVEL, DO RESEARCHERS HAVE EVIDENCE THAT THE POPULATION AVERAGE SALARY HAS INCREASED? NO! CIRCLE APPROPRIATE ANSWER: YES! SPECIFY THE TEST STATISTIC VALUE AND CRITICAL VALUE(S). THEN FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = CRITICAL VALUE(S): REJECTION RULE STATES... (B) DO RESEARCHERS HAVE EVIDENCE THAT THE POPULATION AVERAGE SALARY HAS CHANGED? CIRCLE APPROPRIATE ANSWER: YES! NO! SPECIFY THE TEST STATISTIC VALUE AND CRITICAL VALUE(S). THEN FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = CRITICAL VALUE(S): REJECTION RULE STATES... (C) ESTIMATE THE POPULATION AVERAGE DIFFERENCE WITH 95% CONFIDENCE SHOW THE MID-POINT AND MARGIN OF ERROR. ALSO SPECIFY THE CRITICAL VALUES NEEDED FOR THIS PROCEDURE. CRITICAL VALUE = MID-POINT = MARGIN OF ERROR = UPPER CONFIDENCE LIMIT = LOWER CONFIDENCE LIMIT = 3 HOMEWORK 9 - STAT 3360 - FALL 2015 DUE BY NOVEMBER 10 4. [30 POINTS = 10 + 10 + 10] A STUDY AIMED AT DRAWING CONCLUSIONS ABOUT THE PROPORTION OF CAR COLLISIONS CAUSED BY DRIVER'S TEXTING WAS CONDUCTED. A SAMPLE OF 1,200 CASES WAS ANALYZED. IT TURNED OUT THAT 336 COLLISIONS OCCURRED DUE TO TEXTING WHILE DRIVING. [A] IF THE HYPOTHETICAL PROPORTION OF COLLISIONS CAUSED BY TEXTING IS 25%, FIND THE PARAMETERS OF THE APPROXIMATE NORMAL DISTRIBUTION FOR A SAMPLE PROPORTION. [B] AT THE SIGNIFICANCE LEVEL OF 1%, CAN YOU SAY THAT THERE IS SUFFICIENT EVIDENCE THAT THE POPULATION PROPORTION EXCEEDS 25%? SPECIFY THE TEST STATISTIC VALUE AND CRITICAL VALUE(S). THEN FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = CRITICAL VALUE(S): REJECTION RULE STATES... [C] AT THE SIGNIFICANCE LEVEL OF 1%, CAN YOU SAY THAT THERE IS SUFFICIENT EVIDENCE THAT THE POPULATION PROPORTION DIFFERS FROM 25%? SPECIFY THE TEST STATISTIC VALUE AND CRITICAL VALUE(S). THEN FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = CRITICAL VALUE(S): REJECTION RULE STATES... PROBLEM 1 2 3 4 TOTAL 20 20 30 30 100 POINTS MAXIMUM 4