Let X equal the length of life of a 60-watt light bulb marketed by a certain manufacturer. We do not know the distribution of X except that Var(X) = 1158. Let u be the mean of X. Suppose a random sample of n = 25 bulbs is tested until they burn out, yielding a sample

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Exercise 2
Let X equal the length of life of a 60-watt light bulb marketed by a certain manufacturer.
We do not know the distribution of X except that Var(X) = 1158. Let u be the mean of X.
Suppose a random sample of n = 25 bulbs is tested until they burn out, yielding a sample
mean of x = 1368 hours.
(i) Compute an approximate 95% confidence interval for u.
(ii) Compute an approximate 95% one-sided confidence interval for that provides a
lower bound for u, i.e. compute & such that
P(X - ε ≤ μ) ≈ 0.95.
Transcribed Image Text:Exercise 2 Let X equal the length of life of a 60-watt light bulb marketed by a certain manufacturer. We do not know the distribution of X except that Var(X) = 1158. Let u be the mean of X. Suppose a random sample of n = 25 bulbs is tested until they burn out, yielding a sample mean of x = 1368 hours. (i) Compute an approximate 95% confidence interval for u. (ii) Compute an approximate 95% one-sided confidence interval for that provides a lower bound for u, i.e. compute & such that P(X - ε ≤ μ) ≈ 0.95.
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,