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A random sample of 275 bolts from machine A contained 27 defective bolts... (see attached)

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A random sample of 275 bolts from machine A contained 27 defective bolts, while an independently chosen, random sample of bolts from machine B contained defective bolts. Let be the proportion of the population of all bolts from machine A that are defective, and let be the proportion of the population of all bolts from machine B that are defective. Find a confidence interval for . Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places.

1. What is the lower limit of the 95% confidence interval? _______
2. What is the upper limit of the 95% confidence interval? _______

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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