COMM3710 - Fall 2011 - Section 001 - Lecture Notes - 10/18

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riosjosh

Standard error of percentage
Ö((P*Q)/N)

If you quadruple your sample size then your error will be cut in half.

Where is there the biggest error (60-40, 30-70, 10-90, 50-50)?
At 50-50 there is the biggest error (0.25). This is because at this level it is a toss up or almost guessing. We have the most confidence at the 10-90 level in this sample. If everyone more or less agrees then we should be pretty confident. The math reflects this logic.

Comm 3710 Standard Error for Percentage
1. In response to a poll question asking whether parking on campus was a serious problem on the U of U campus, 18 students said they “strongly disagreed,” 27 said they “disagreed,” 19 said they “agreed,” and 28 said they “strongly agreed”
Is there a significant difference between the responses?

H0: F1 = F2 = F3 = F4 ; or there is no difference between what students thing about parking
H1: Not H0 ; or Students feel differently about the parking problem on campus
Decision Rule: df = (K-1) = 4-1 = 3 the critical value is 7.82

Students
Fo
Fe
(Fo-Fe)
(Fo-Fe)^2
(Fo-Fe)^2/Fe
Strongly disagree
18
23
-5
25
1.09
Disagree
27
23
4
16
0.70
Agree
19
23
-4
16
0.70
Strongly Agree
28
23
5
25
1.09
Total:
92


Calculated value:
3.57

Failed to reject the null; there is no difference in student responses.

Standard error for percentage polls
Public opinion polls often ask people if they approve or disapprove, vote for or against, and so on. If this is the case we can use the standard error of percentage formula to calculate how good of an estimator the statistic is:
The Formula is : Standard Error for Percentage Polls= Ö((P*Q)/N)
Where s is the standard error, p and Q are the percentage of the population for the two categories and n is the number in the sample.

3. In a national poll conducted in March, 66% of Americans said that they worry “a great deal” about the quality of the environment under the Bush administration. The Poll was based on telephone interviews with 400 adults.
Calculate the margin of error (confidence interval) at the 68%, 95%, and 99% level.

N=400; P=.66; Q=.34