Statistics-A SAMPLE OF 16 CAR POLICIES WAS DRAWN FOR THE ANALYSIS OF CAR

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 MID-POINT 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..