Question: 1. The poll claims that 70% of the population is for a new amendment. A random sample of 49 people showed that 27 voted in favor of the new amendment. Give a 95% confidence interval. Give lower limit and upper limit accurate to four decimals.

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Answer: 1. ans: Proportion, p=27/49=0.55
Margin of error, e= sqrt(pq/N)*z_c
Here, z_c=1.96 (At 95% confidence interval)
N=49
e= sqrt(0.55*0.45/49)*1.96=0.1392
Confidence interval, (p-e, p+e)=(0.55-0.1392, 0.55+0.1392)=(0.4108, 0.6892)

lower limit =0.4108
upper limit =0.6892

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