Question

A)

According to the results of the 2004 presidential election, 50% of New Yorkers voted for Kerry. Imagine the set of all possible random samples of size 36 from all New Yorkers who voted. For each sample of size 36, the value of the sample proportion  is the percentage of the people in the sample that voted for Kerry.

What would the mean of all these sample proportions be? Use 1 decimal places, for example, 0.1

B) What would the standard deviation of all these sample proportions be? Use 3 decimal places, for example, 0.111

C)

Would the distribution of all these sample proportions be approximately Normal?

		Yes, because there are more than 10 successes and 10 failures.
		No, because the candidate you vote for the presidential election is a categorical variable.
		Yes, because we have a sample size of 36.
		Yes, because the sample proportions is a continuous random variable.
		Not enough information is provided.

Answer 1

A) Given that, population proportion (p) = 0.50

sample size (n) = 36

The mean and standard deviation of the sampling distribution of the sample proportion are,

Therefore, the mean of all these sample proportions is 0.5

B) The standard deviation of all these sample proportions is 0.083

C) Here, np = 36 * 0.5 = 18 and n(1-p) = 36 * 0.5 = 18 both are greater than 10, so the distribution of all these sample proportions is approximately normal.

Answer : Yes, because there are more than 10 successes and 10 failures.