Page 366 - DMTH404_STATISTICS

Statistics

Notes 25.4 Self Assessment

1. Fill in the blanks:
(i) The positive square root of variance of a sampling distribution is known as ...... .
(ii) The standard error of X varies ...... with standard deviation and ...... with sample
size.
(iii) The sampling distribution of proportion would be approximately normal when n is
greater than or equal to ...... .
2
(iv) The mean and variance of a  -variate depend upon its ...... .

25.5 Review Questions

1. We are given the fact that 30% of all patients admitted to a medical clinic fail to pay their
bills and the bills are eventually forgiven. If the clinic treats 2000 different patients over a
period of one year, what is the expected number of bills that would have to be forgiven. If
X is the number of forgiven bills in the group of 2000 patients, find the variance and
standard deviation of X. What can you say about the probability that X will exceed 700?
2. A random sample of 10 observations is to be taken from a normal population with variance
equal to 16. What is the probability of obtaining a sample with variance greater than 20?
 2
Hint : Use - distribution.

3. Two independent random samples of sizes 15 and 12 are taken from a normal population.
Find the probability that the ratio of their variances is greater than 3. Assume that the
variance of the sample of size 15 is greater than the variance of the other.

Answers: Self Assessment

1. (i) standard error (ii) directly, inversely (iii) 50 (iv) parameter

25.6 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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