Question

In: Statistics and Probability

Suppose 40% of the registered voters in a country are Republican. If a sample of 815...

Suppose 40% of the registered voters in a country are Republican. If a sample of 815 voters is selected, what is the probability that the sample proportion of Republicans will differ from the population proportion by more than 4%? Round your answer to four decimal places.

Expert Solution

Lower = 812(0.4 - 0.04 ) = 815*0.36 = 293.4

Upper = 812(0.4 + 0.04 ) = 815*0.44 = 358.6

The following information has been provided about the population proportions and the sample size:

Population Proportion =	0.4
Sample Size =	815

We need to compute Based on the information provided, the population men of sample proportions and the corresponding standard error are:

Observe that:

which indicates that the assumption for normal approximation for the sampling distribution is met.

Since we need to use a continuity correction, we need to use the factor to adjust the end points of the end points of the probability intervals, so the new limits are:

Now, the following is obtained using normal approximation:

orchestra answered 2 years ago

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