Test of Hypothesis

Clubs with hollow heads and very thin faces can

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Unformatted text preview: level of signiﬁcance. Stated more completely, we conclude that the mean burning rate diﬀers from 50 cen\$meters per second, based on a sample of 25 measurements. Dr. Hatem Elayat, AUC 19 Tests Concerning the Mean of a Normal Popula\$on Case 2: Unknown Variance Procedure 1.Null Hypothesis H0 : µ = µ0 2. Alterna\$ve Hypotheses a) H1 : µ > µ 0, b) H1 : µ < µ 0, c ) H1 : µ ≠ µ 0, X − µ0 3. Test Sta\$s\$c t = s/ n 4. Cri\$cal Region Reject if t > tα ,n −1 Dr. atem layat, Reject if t < H− tα En −1 AUC , Reject if t > tα / 2,n −1 20 Example The increased availability of light materials with high strength has revolu\$onized the design and manufacture of golf clubs, par\$cularly drivers. Clubs with hollow heads and very thin faces can result in much longer tee shots, especially for players of modest skills. This is due partly to the “spring ­like eﬀect” that the thin face imparts to the ball. Firing a golf ball at the head of the club and measuring the ra\$o of the outgoing velocity of the ball to the incoming velocity can quan\$fy this spring ­like eﬀect. The ra\$o of veloci\$es is called the coeﬃcient of res\$tu\$on of the club. An experiment was performed in which 15 drivers produced by a par\$cular club maker were selected at random and their coeﬃcients of res\$tu\$on measured. In the experiment the golf balls were ﬁred from an air cannon so that the incoming velocity and spin rate of the ball could be precisely controlled. It is of interest to determine if there is evidence (with α = 0.05 ) to support a claim that the mean coeﬃcient of res\$tu\$on exceeds 0.82. Dr. Hatem Elayat, AUC 21 The observa\$ons follow: Example (Contd.) Dr. Hatem Elayat, AUC 22 Data: Example (Contd.) X...
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