The Centers for Disease Control periodically takes large randomized surveys to t

Question

The Centers for Disease Control periodically takes large randomized surveys to track of health of Americans. In a survey of 11, 207 adults in 1980, 47% were overweight. In a survey of 4431 adults in 2004, 66% were overweight. Give a 95% confidence interval for difference between the true proportions of overweight Americans in 2004 and 1980. (a) Find the point estimate. (b) Find the standard error of this estimate. (c) Find the margin of error for a 95% confidence interval (d) Find a 95% confidence interval for difference between the true proportions of overweight Americans in 2004 and 1980.

Explanation / Answer

Part-a :

Points estimate of difference in proportion=phat1-phat2=0.47-0.66=-0.19

Part-b

Standard error of difference in proportion SED=sqrt(phat1*(1-phat1)/n1+ phat2*(1-phat2)/n2)

=sqrt(0.47*(1-0.47)/11207+0.66*(1-0.66)/4431))

=0.0085

Part-c

For 95% confidence interval critical z=1.96

So margin of error E=1.96*SED=1.96*0.0085=0.0167

Part-d

95% confidence interval for difference =( phat1-phat2)±E

=-0.19±0.0167

=(-0.2067        -0.1733)

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