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Unformatted text preview: 2. An opinion poll is requested to estimate the proportion (p) of her constituents who favour the discrimination
of certain narcotics violations. How large a sample will be needed to be able to assert with 95% conﬁdence
that the error of estimation is no more than 0.03, if
(a) the poll has no idea about p,
(b) there are reasons to believe that p will be approximately 0.25?
3. Past experience has shown that 10% of the recipients of loans from a particular mortgage-lending institution
default on their mortgarge within the ﬁrst 3 years. The mortgage company has observed, however, that the
proportion of default seems to be increasing. If evidence can be obtained that the proportion of customers
who default on their mortgage is now greater than 0.1, the company will review and revise its guidelines for
granting mortgages. A random sample of 200 customers who received loan 3 years ago indicated that 30 of
them defaulted on their mortgage. Test at 1% signiﬁcance level whether there is suﬃcient evidence indicating
that the proportion of default is on the increase.
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