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 = 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

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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 = 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
ɛ
P(X - ≤ μµ)≈ 0.95.
Transcribed Image Text: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 = 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 ɛ P(X - ≤ μµ)≈ 0.95.
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