Page 359 - DMTH404_STATISTICS

Unit 24: Sampling Distributions

24.6 Self Assessment Notes

1. State whether the following statements are True or False:
(i) Mean of the sample means is equal to population mean.
(ii) Random variable of a sampling distribution is called a statistic.

(iii) The sampling distribution of X is normal if the drawn samples are of size 20.
(iv) When population is large, the finite population correction (fpc) is negligible, i.e.,
approximately equal to zero.

(v) In order that a statistic t follows a t - distribution, the sample should have been
obtained from a normal population.

24.7 Review Questions

1. Explain the concept of sampling distribution of a statistics.

2. Find the mean and standard error of sample mean in (a) Simple random sampling with
replacement, (b) Simple random sampling without replacement.
3. Distinguish between:

(a) Parameter and Statistic.
(b) Sampling distribution and Probability distribution.
(c) Standard deviation and Standard error.
4. (a) Distinguish between sampling with replacement and sampling without replacement.
How many random samples of size n can be drawn from a population consisting N
items if the sampling is done (i) with replacement, (ii) without replacement?

(b) What is the variance of the sample mean if sampling is done (i) with replacement (ii)
without replacement?
(c) Under what conditions do the answers in (b) approach each other?

5. If X (i = 1, 2, ..... n) are n independent normal variates with respective mean m and standard
i i
deviation s , then show that the variate u = åX is normally distributed with mean å and
i i mi
2
variance ås .
i
Answers: Self Assessment
1. (i) T (ii) T (iii) F (iv) F (v) T

24.8 Further Readings

Books Sheldon M. Ross, Introduction to Probability Models, Ninth Edition, Elsevier
Inc., 2007.

Jan Pukite, Paul Pukite, Modeling for Reliability Analysis, IEEE Press on
Engineering of Complex Computing Systems, 1998.

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