Question

According to a Time Magazine/ABT SRBI poll conducted by telephone during October 9–10, 2011, 73% of adults age 18 years and older said that they are in favor of raising taxes on those with annual incomes of $1 million or more to help cut the federal deficit (Time, October 24, 2011). Assume that this percentage is true for the current population of all American adults age 18 years and older. Let p̂ be the proportion of American adults age 18 years and older in a random sample of 882 who will hold the above opinion. Find the mean and standard deviation of the sampling distribution of p̂ and describe its shape. Round your answer for the standard deviation to four decimal places.

μp̂ =

σp̂ =

Answer 1

The mean and the standard deviation of the sampling distribution is calculated as:

Since the population proportion p=0.73 hence Mean is calculated as the 0.73

and Standard deviation is calculated as:

Now To check whether the distribution is normal following condition must be satisfied:

1) p*(1-p)*n>10

so,0.73(1-0.73)*882=173.84, so the condition is satisfied.

2) The sample should be randomly taken from a large population hence this condition is also satisfied.

3) The sample size >30

So, since all the conditions are satisfied we can say that the population is normally distributed and will have a bell-shaped distribution.