022 0022 round to 3 decimal places question 3 what is

.022
0.022
(Round to 3 decimal places)
Question 3 . What is the probability that the proportion of these 400 freshmen that return to the same school for their

ST 350-002 HW #8 Spring 2016
[4/27/2016 11:36:43 AM]
3. 2/2 points | Previous
Answers
My Notes
4. 3/3 points | Previous
Answers
My Notes
sophomore year is less than 0.68 ?
.0115
0.0115
(Round to 4 decimal places)
Solution or Explanation
NOTE: The solutions shown below assumes that the Department of Education proportion of college freshmen that return
for their sophomore year is p = 0.70 and the size of the random sample is n = 450. The proportion in question 3 is
assumed to be 0.72. Your version of the problem may have different values.
Question 1: E(phat) = p = 0.70
Question 2: SD(phat) = sqrt[p*(1-p)/n] = sqrt[0.70*(1-0.70)/450] = 0.022
Question 3: The sampling distribution model for phat is N(0.70, 0.022)
P(phat < 0.72) = P[(phat-0.70)/0.022 < (0.72-0.70)/0.022] = P[z < 0.02/0.022] = P[z < 0.91] = 0.8186
Just before a city referendum on a school budget, a local newspaper polls 470 voters in an attempt to predict whether the
budget will pass. Suppose that, unknown to everyone, the budget actually has the support of 54 % of the voters.
Question . What is the probability the newspaper's sample will lead the newspaper to predict defeat of the referendum, that
is, what is the probability that the newspaper's sample results in a sample proportion
p ̂
less than 0.50 in favor of the
referendum?
.0409
0.0409
(calculate the standard deviation of
p ̂
to 4 decimal places, round your final answer to 4 decimal places).
Solution or Explanation
NOTE: the solution shown below assumes that the size of the newspaper's sample is n = 470 and that the budget has the
support of 54% of the population, that is, p = 0.54. The values in your version of the problem may differ.
E(
p ̂
) = p = 0.54; SD(
p ̂
) = sqrt[p*(1-p)/n] = sqrt[0.54*0.46/470] = 0.0230. So the sampling distribution model for
p ̂
is
p ̂
~N(0.54, 0.0230).
Therefore,
P(
p ̂
< 0.50) =
P[(
p ̂
-0.54)/0.0230 < (0.50-0.54)/0.0230]=
P[z < -1.74] = 0.0409
The concept of sampling error is discussed in the section Understanding the Margin of Sampling Error in the middle of
page 4 in the document New York Times Polling Standards (pdf). The third paragraph in this section is discussing the
sampling distribution of , where is the sample proportion of items in a sample that has the characteristic of
interest.
Question 1 . If, as mentioned in the third paragraph, "the truth is 40%" (that is, the value of the population proportion p is

ST 350-002 HW #8 Spring 2016
[4/27/2016 11:36:43 AM]
5. 2/2 points | Previous My Notes
p = .40), select the choice below that represents the sampling distribution model for based on a sample of size n =
1000.
It may assist you in answering the following questions to first verify the statement made in the last sentence of the third
paragraph: "And 95 out of those 100 separate poll measures would be between 37% and 43%". Recall that the population
proportion p is .40 and n = 1000.