STA3032 Quiz 8 Solutions

STA3032 Quiz 8 Solutions - random variable c Normal...

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STA3032 QUIZ 8 SOLUTIONS FALL 2011 Problem 10.95 [page 566] The mean breaking strength of cotton threats must be at least 215 grams, for the threat to be used in a certain garment. A random sample of 50 measurements on a certain threat gave a mean breaking strength of 210 grams and a standard deviation of 18 grams. Should this thread be used on the garment? If the mean strength of cotton is at least 215, i.e., μ ≥ 215, the threat can be used, whereas if μ < 215 it should not be used. Then, 1. Hypotheses of interest are Ho: μ ≥ 215 vs. Ha: μ < 215 or equivalently, Ho: μ = 215 vs. Ha: μ < 215. 2. Assumptions: a. SRS? Yes, stated in the problem. b. Quantitative rv? Yes, strength of threads is a quantitative
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Unformatted text preview: random variable. c. Normal Distribution? Not stated, assume it is. d. Large sample? Yes, n = 50 > 30 so CLT may be used. All assumptions seem to be satisfied. 3. Test statistic: Since σ is unknown the test statistic is ( n 1 ) X T ~ t S / n μ--= 4. P-Value: Given n = 50, X 210 = and S = 18, cal 210 215 T 1.964 18 / 50-= = -. Because Ha: μ < 215, p-value = P(T (49) ≤ – 1.96) = 0.025 (approximately) 5. Decision: Assuming α = 0.05, we reject Ho. 6. Conclusion: The observed data indicate that the mean breaking strength of the thread is less than 215 and hence should not be used on the garment (p-value = 0.025)....
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