Question

# A recent poll found that 65% of registered voters in the U.S. are not satisfied with...

A recent poll found that 65% of registered voters in the U.S. are not satisfied with the U.S. Congress. A sample of 1293 registered voters was polled. Based on this information answer the following: First, the population of interest. Second, state the sampling distribution for p-hat. Third, state the parameters to the sampling distribution and round to 4 decimal place, as needed.

From the given information,

a. Population of interest is given by,

All registered voters in the U.S. that are not satisfied with the U.S. Congress.

b. Suppose, P=Population proportion

Now, As n=1293 which is sufficiently large, Hence Sampling distribution of p-hat is approximately normal with mean=P and Variance=(P*(1-P))/n

c.

Parameters of the sampling distribution,

Mean=P=0.65

Variance=(P*(1-P))/n=(0.65*(1-0.65))/1293

Variance=0.0002

Hence,

Standard deviation=Squareroot(Variance)=Squareroot (0.0002)

Standard deviation=0.0133

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