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=0.01 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)	81	78	83	80	87	87	89	94
Score (new design)	78	82	78	76	92	83	88	89

WITH EXPLAINATION OF WORK

Answer 1

Lolim: Jo check whether the golfers can lower their scores by _wing the manufactures_newly designed_golf clubs - or not. alien : The score of 8 golfers after t before_wing the newly - designed_gofclubs £lom the gaien information wecise paired t-test for testing the hypothesis , 10 Parameters: het Hy d Mz be the mean scores of golfers ofter wing the newly golfclubs before using the newly golfelubs respectiely iT and we Hypothesis ; Ho • Dhe mean scores of golfers after f before using newly golfelubs do not differ significantly or is same Hei The mean scores of golfers after using the newly golfelubs is less than that of the ob mean Scores of golfers before using the newly golfelubo. Mathematically || 40 : M1 = H2V:l'18 M1: y = 12. VIS. | Butin paired t test we nove a quantity di which is the difference in pores scores of the goffers | Let'di = score after - score" before." Loo let xi bete ocores after using the newly golfclube 4 Yi be the scores before using the newly gólfelubs eco bere Cxi, Yi) be a bivariate. Mormol tendon variable wito mean of x as MX = Ms & that of Y as My = M2 with

variances of x as ox ² of off as ry. so here di ~ N( Md, od 2) where Hd & MX - MY.. - MI - M2. Hypothesis become l Ho: Md cd. inkit lids l Hl: Md co. Jest statistici trala 5 - Md atin-1,2)._ Tu vinde illis mollis et Violin its too lan i hered to meen of differences of the samplein : I sds sample standard deviation of differences. so now, we first calculate ă sed ' A Golfer boScore (new) = xi balcore Cold) - Yi I1| 2 | 3 | 4 | 5 | 617181 | 78 | 82 | 78 | 76 | 92 | 83 | 88 89 181 | 78 | 83 | 80 | 87 | 87 | 89 94 1-3 4 -5 45-4-1 -5| ā = Edi = -13 =-1.625 n 15.9821 8d = II di -12 n-1 sd = 3.9978 Now, under Ho, Md zo teal = -1.625 3.9978 18

tal = -1.625 1:4134 I tal = -1. 1497 Decision : Reject Hoit tray ? -ten-1,2) I here tiny, as = + 18-1,0.01) = +17,0.01) = 2.9979 here tal = -1:1492_ > -ten-t, 2) = 2.9979. Loo accept ho U Conclusion : The scores of golfers after & before using newly golfelubs may not differ signifičantly. There is not enough evidence to support the manufacturer's claim.