4.2.9. Let X₁, X2,..., X9 be a random sample of size 9 from a distribution that is N(μ, 0²). (a) Ifo is known, find the length of a 95% confidence interval for μ if this interval is based on the random variable √9(x-μ)/o. (b) Ifo is unknown, find the expected value of the length of a 95% confidence interval for μ if this interval is based on the random variable √9(X-μ)/S. Hint: Write E(S) = (o/√n - 1)E[((n − 1)S²/0²)¹/2]. - (c) Compare these two answers.

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4.2.9. Let X₁, X2,..., X9 be a random sample of size 9 from a distribution that is
N(μ, 0²).
(a) Ifo is known, find the length of a 95% confidence interval for
is based on the random variable √9(X -μ)/o.
fl
if this interval
(b) Ifo is unknown, find the expected value of the length of a 95% confidence
if this interval is based on the random variable √9(x-μ)/S.
Hint: Write E(S) = (o/√n - 1)E[((n − 1)S²/0²)¹/2].
interval for
fl
(c) Compare these two answers.
Transcribed Image Text:4.2.9. Let X₁, X2,..., X9 be a random sample of size 9 from a distribution that is N(μ, 0²). (a) Ifo is known, find the length of a 95% confidence interval for is based on the random variable √9(X -μ)/o. fl if this interval (b) Ifo is unknown, find the expected value of the length of a 95% confidence if this interval is based on the random variable √9(x-μ)/S. Hint: Write E(S) = (o/√n - 1)E[((n − 1)S²/0²)¹/2]. interval for fl (c) Compare these two answers.
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