A golf club manufacturer claims that golfers can lower their scores by using the manufacturer's newly designed golf clubs. The table shows the scores of 10 golfers while using the old design and while using the new design on the same golf course. At \(\alpha=0.05\), can you support the manufacturer's claim?

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Golfer Score (old design) 1 2 3 4567 8 9 10 89 84 96 74 91 85 95 82 92 81 Score (new design) 83 83 92 76 91 80 87 85 90 77