Question

The proportion of voters who voted for Donald trump in the last Presidential election was .46. Suppose we obtain a random sample of n =400 voters who voted in the last Presidential election, and phat is the proportion of voters in the sample who voted for Trump. What is the standard deviation of the sampling distribution of phat for a sample of size 400 ?

  

      

	a.	3.16
	b.	9.97
	c.	.498
	d.	.0249

Answer 1

Given that, the proportion of the population that voted for Trump in the last presidential election is 0.46.

So, here our p=0.46.

Now, we obtain a random sample of n=400 voters, who voted in the last election, and phat is the proportion of voters in this sample, who voted for Trump.

Now, to find the standard deviation of the sampling distribution of phat.

Now, we know that the sampling distribution of phat will have a mean equal to p, and standard deviation equal to

sqrt((p*(1-p)/n).

So, the required standard deviation is

=sqrt(0.46*(1-0.46)/400)

=sqrt(0.46*0.54/400)

=sqrt(0.2484/400)

=sqrt(0.000621)

=0.0249.

So, the standard deviation of the sampling distribution of phat is (d) 0.0249.