An interactive poll found that 324 of 2,266 adults aged 18 or older have at least one tattoo.
?(a) Obtain a point estimate for the proportion of adults who have at least one tattoo.
?(b) Construct a 90 ?% confidence interval for the proportion of adults with at least one tattoo.
?(c) Construct a 98 ?% confidence interval for the proportion of adults with at least one tattoo. ?
(d) What is the effect of increasing the level of confidence on the width of the? interval?
Solution:-
a) The point estimate for the proportion of adults who have at least one tattoo is 0.14298.
b) 90% confidence interval for the proportion of adults with at least one tattoo is C.I = (0.1309, 0.1551).
C.I = 0.14298 + 1.645 × 0.00735
C.I = 0.14298 + 0.0121
C.I = (0.1309, 0.1551)
c) 98% confidence interval for the proportion of adults with at least one tattoo is C.I = (0.1259, 0.1601).
C.I = 0.14298 + 2.327 × 0.00735
C.I = 0.14298 + 0.0171
C.I = (0.1259, 0.1601)
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