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Example In a sample of 900 stock-holders of companies, 400 stated that their major aim in holding stocks is capital appreciation. What is the 90% confidence range within which lies the population proportion of stock-holders who hold stocks for capital appreciation ?

Solution: The 90% confidence range is given by P' ± 1.64 S.E. where S.E. =

Now P' =

Hence the range is given by

Hence the range is 0.4444 + 0.0272 = 0.4716 and

0.4444 - 0.0272 = 1.4172

ie. ( 0.4172 to 0.4716 ).

*   Note that when we do not know po and qo then we can use p' and q' in their places respectively.

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Example Out of consignment of 10000 tennis balls, 400 were selected randomly and examined. it was found that 20 of these were defective. How many defective balls you can reasonably expect to have in the whole consignment at 95% confidence level ?

Solution: P' = = 0.05 and q' = 1 - p = 0.95

The limits are ( at 95% confidence level ) = p' ± 1.96 S.E.

where S. E. =

Therefore, 0.05 ± 1.96 ´ 0.01089 i.e. 0.05 ± 0.0213

Therefore p' lies between 0.0713 to 0.0287.

The expected number lies between

NP' = 10000 ´ 0.0713 = 7130 and

NP' = 10000 ´ 0.0287 = 2870.

Index

Chapter 1