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solution-HW2c

# solution-HW2c - Solution for ST516 HW2 2.11 The breaking...

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Solution for ST516 HW2 2.11. The breaking strength of a fiber is required to be at least 150 psi. Past experience has indicated that the standard deviation of breaking strength is σ = 3 psi. A random sample of four specimens is tested. The results are y 1 =145, y 2 =153, y 3 =150 and y 4 =147. (a) State the hypotheses that you think should be tested in this experiment. H 0 : µ = 150 H 1 : µ > 150 (b) Test these hypotheses using α = 0.05. What are your conclusions? n = 4, σ = 3, y = 1/4 (145 + 153 + 150 + 147) = 148.75 148.75 150 1.25 0.8333 3 3 2 4 o o y z n µ σ = = = = − Since z 0.05 = 1.645, do not reject. (c) Find the P -value for the test in part (b). From the z- table: ( )( ) 1 {1 0.7967 2 3 0.7995 0.7967 } 0.7986 P + = (d) Construct a 95 percent confidence interval on the mean breaking strength. The 95% confidence interval is ( ) ( ) ( ) ( ) 2 3 96 . 1 75 . 148 2 3 96 . 1 75 . 148 2 2 + + µ σ µ σ α α n z y n z y

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