Question

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.

Answer #1

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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