Question

In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is

Answer 1

The 95% confidence interval of voters not favoring the incumbent is (0.0706, 0.1294).

Sample size, n=400

Sample proportion, p = 40 / 400

= 0.1

We use normal approximation, for this, we check that both np and n(1-p) >5.

Since n*p = 40 > 5 and n*(1-p) = 360 > 5, we can take binomial random variable as normally distributed, with mean = p = 0.1 and standard deviation  = root( p * (1-p) /n )

= 0.015

For constructing Confidence interval,

Margin of Error (ME) =  z x SD = 0.0294

95% confidence interval is given by Sample Mean +/- (Margin of Error)

0.1 +/- 0.0294 = (0.0706 , 0.1294)

Learn more about Margin of Error here brainly.com/question/15691460

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