handout10sol

handout10sol - STAT 345 Handout 10 solutions Hypothesis...

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Unformatted text preview: STAT 345 - Handout 10 solutions Hypothesis Tests Based on sections: 9.1 – 9.2 1. A machine is set to produce bolts with a mean length of 1 inch. Bolts that are too long or too short do not meet the customer’s specifications and must be thrown out. To avoid producing too many rejects, the bolts produced by the machine are sampled from time to time and tested as a check to determine whether the machine is still operating properly. Suppose 50 bolts have been sampled and ¯ x = 1 . 02 inches and s = 0 . 04 inch. Does the sample evidence indicate that the machine is producing bolts with a mean length not equal to 1 inch? That is, is the production process out of control? (a) H : μ = 1 . 00 ,H a : μ 6 = 1 . 00. Is the mean different from 1.00 in.? (b) Z = ¯ X- μ s/ √ n = 1 . 02- 1 . 00 . 04 / √ 50 = 3 . 54 (c) p-value = 2 P ( Z <- 3 . 54) = 2(0 . 000200) = 0 . 0004 (two-tailed p-value) (d) Since the p-value is small (0 . 0004 < . 01 at the α = 0 . 01 signifi- cance level), we reject...
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handout10sol - STAT 345 Handout 10 solutions Hypothesis...

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