(a) Discuss the two expressions -2 (x;- F )² and -7), both of which are uscd (n –1)=1 (n-1 to measure the spread of a set of observations x1, x2, . . . , x. n=1 (b) A random sample of n observations is taken from a distribution; the sum of the observations is t, and the sum of the squares of the observations is 12. Explain how to estimate the mean and the variance of the distribution from which the random sample was taken. (c) Given the random sample described in part (b), write down expressions (based on t1 and t2) for estimates of the mean and variance of the mean of a further, independent, random sample of size m , from the original distribution. (d) Given that n = 25, 1, = 400 and 1, = 8800, construct a 99% confidence interval for the mean of the distribution, and use it to test whether or not this mean could be 20. %3D
(a) Discuss the two expressions -2 (x;- F )² and -7), both of which are uscd (n –1)=1 (n-1 to measure the spread of a set of observations x1, x2, . . . , x. n=1 (b) A random sample of n observations is taken from a distribution; the sum of the observations is t, and the sum of the squares of the observations is 12. Explain how to estimate the mean and the variance of the distribution from which the random sample was taken. (c) Given the random sample described in part (b), write down expressions (based on t1 and t2) for estimates of the mean and variance of the mean of a further, independent, random sample of size m , from the original distribution. (d) Given that n = 25, 1, = 400 and 1, = 8800, construct a 99% confidence interval for the mean of the distribution, and use it to test whether or not this mean could be 20. %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1
(a) Discuss the two expressions -x;- )² and
E(x;- )², both of which are used
(n-1) i=1
to measure the spread of a set of observations x1, x2, . .., X.
(b) A random sample of n observations is taken from a distribution; the sum of the
observations is t, and the sum of the squares of the observations is 12. Explain how to estimate
the mean and the variance of the distribution from which the random sample was taken.
(c) Given the random sample described in part (b), write down expressions (based on 11
and t2) for estimates of the mean and variance of the mean of a further, independent, random
sample of size m , from the original distribution.
(d) Given that n = 25, 1, = 400 and t2 = 8800, construct a 99% confidence interval for the
mean of the distribution, and use it to test whether or not this mean could be 20.
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