Question

A golf club manufacturer claims that golfers can lower their scores by using the manufacturer's newly designed golf clubs. Eight golfers are randomly selected and each is asked to give his or her most recent score. After using the new clubs for one month, the golfers are asked again to give their most recent score. The scores for each golfer are given in the table below. Is there enough evidence to support the manufacturer's claim?

Let

d=(golf score after using the newly designed golf clubs)−(golf score before using the newly designed golf clubs). Use a significance level of α=0.05 for the test. Assume that the scores are normally distributed for the population of golfers both before and after using the newly designed clubs.

Golfer	1	2	3	4	5	6	7	8
Score (old design)	88	74	84	85	82	80	79	82
Score (new design)	83	77	82	80	85	79	78	76

Answer 1

SOLUTION-

LET BE THE SCORE FOR NEW DESIGN AND BE THE SCORE FOR OLD DESIGN. THE HYPOTHESIS WE FRAME AS PER THE MANUFACTURER'S CLAIM IS:

[CLAIM]

AS THE SAMPLES ARE DISTRIBUTED NORMALLY, WE PERFORM A TWO SAMPLE-T TEST AND USE MINITAB-16 FOR CALCULATION.

STEPS: ENTER THE DATA> STAT> BASIC STATISTICS> TWO SAMPLE-T> SELECT THE DIFFERENT SAMPLES> UNDER 'OPTIONS', SET THE CONFIDENCE LEVEL 95.0 AND ALTERNATE AS 'LESS THAN'> OK

THE TEST STATISTIC IS T= -0.94 AND THE CORRESPONDING P-VALUE IS 0.183

AS P-VALUE> 0.05, WE FAIL TO REJECT THE NULL HYPOTHESIS.

HENCE, THERE IS NOT SUFFICIENT EVIDENCE TO SUPPORT THE MANUFACTURER'S CLAIM.

****IN CASE OF DOUBT, COMMENT BELOW. ALSO LIKE THE SOLUTION IF POSSIBLE.