Math Problem Statement
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Topic 6 Homework (Nonadaptive) Question 10 of 11 (1 point)|Question Attempt: 1 of Unlimited
1 2 3 4 5 6 7 8 9 10 11 Question 10 A random sample of 275 bolts from machine A contained 22 defective bolts, while an independently chosen, random sample of 250 bolts from machine B contained 17 defective bolts. Let p1 be the proportion of the population of all bolts from machine A that are defective, and let p2 be the proportion of the population of all bolts from machine B that are defective. Find a 95% confidence interval for −p1p2. Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. (If necessary, consult a list of formulas.)
Lower limit: Upper limit:
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Intervals
Proportions
Formulas
p1 = x1/n1
p2 = x2/n2
Standard Error = sqrt[(p1(1-p1)/n1) + (p2(1-p2)/n2)]
Confidence Interval = (p1 - p2) ± z * SE
Theorems
Central Limit Theorem
Z-distribution for Confidence Intervals
Suitable Grade Level
Grades 10-12 (Advanced High School)
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