2. [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. (A) A T 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 = C RITICAL VALUE(S): R EJECTION RULE STATES... (B) A T 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! S HOW THE CRITICAL VALUE(S) NEEDED FOR YOUR DECISION AND FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = C RITICAL VALUE(S): R EJECTION RULE STATES... 3. [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. (A) A T THE 1% SIGNIFICANCE LEVEL, DO RESEARCHERS HAVE EVIDENCE THAT THE POPULATION AVERAGE SALARY HAS INCREASED? CIRCLE APPROPRIATE ANSWER: YES! NO! SPECIFY THE TEST STATISTIC VALUE AND CRITICAL VALUE(S). THEN FORMULATE THE REJECTION RULE. TEST STATISTIC VALUE = C RITICAL VALUE(S): R EJECTION 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 = C RITICAL VALUE(S): R EJECTION RULE STATES... (C) ESTIMATE THE POPULATION AVERAGE DIFFERENCE WITH 95% CONFIDENCE S HOW THE MIDPOINT AND MARGIN OF ERROR. A LSO SPECIFY THE CRITICAL VALUES NEEDED FOR THIS PROCEDURE. C RITICAL VALUE = MID-POINT = M ARGIN OF ERROR = UPPER CONFIDENCE LIMIT = LOWER CONFIDENCE LIMIT = 3 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 = C RITICAL VALUE(S): R EJECTION 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 = C RITICAL VALUE(S): R EJECTION RULE STATES