Tests Do Keypad O Tables MATTHEW STEWAI Step: (10 points) PROBLEM Agolf club man

Question

Tests Do Keypad O Tables MATTHEW STEWAI Step: (10 points) PROBLEM Agolf club manufacturer claims that gollers can ower their scores by using the manufac ly designed golf clubs. Eight Rorers are randomly selected and each is asked to give his or her most recent score. After using the new chbs 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 manufacturers Let d- (golf score using the newt golr clubs) -(golf score before using the newly designed golf cubs). Use a a significance level of a-0.05 for the test. Assume that the scores are nommally distributed for the population of golfers both before and aner using the newly designed chubs. 76 88 91 77 84 78 92 91 Score (old design) 75 90 76 sa 77 86 Score (new design) State the null and atemative bypotheses for the test.

Explanation / Answer

Solution

Let X = score with the new design club, Y = score with the old design club and D = X – Y.

Given X and Y are normal and assuming they are independent, D ~ N with mean and variance µ, 2 respectively, say.

Null hypothesis: H0 : µ = 0 Vs Alternative: HA : µ < 0.

Test statistic: t = (n)(Dbar - 0)/s, where n = sample size (8), Dbar = average and s = standard deviation of D from the given sample data.

= (8)(- 12/8)/3.279 = - 1.294.

Distribution:

Under H0, t ~ tn-1 = t7

Decision:

Reject H0, if tcal < tcrit, tcrit = lower 5% (given = 0.05) point of t7 = - 1.894.

Since - 1.294 > - 1.894, H0 accepted.

Conclusion:

Statistical evidence is not sufficient enough to validate the club manufacturer’s claim.

DONE

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