Question

1. Citizen registration and voting varies by age and gender. The following data is based on registration and voting results from the Current Population Survey following the 2012 election. A survey was conducted of adults eligible to vote. The respondents were asked in they registered to vote. The data below are based on a total sample of 760. We will focus on the proportion who voted for males and for females. There is no expectation that one group is more likely to vote. 

Gender	Voted	Not Voted	Total
Males	217	147	364
Females	252	144	396
Total	399	361	760

If we want to calculate a confidence interval of the difference of two proportions, what is the standard error? 

• SQRT{1,5962*4038)/364+ (-6364*3636)/396] 

• [(.5962".4038/364+ (-6364*3636/396]^2 

• SQRT{,4861)/364 + (4861/396] 

• SQRT[(6171*3829)/364 + (61713829)396]
  

2. Citizen registration and voting varies by age and gender. The following data is based on registration and voting results from the Current Population Survey following the 2012 election. A survey was conducted of adults eligible to vote. The respondents were asked in they registered to vote. The data below are based on a total sample of 760. We will focus on the proportion who voted for males and for females. There is no expectation that one group is more likely to vote.

Gender	Voted	Not Voted	Total
Males	217	147	364
Females	252	144	396
Total	399	361	760

What is the Bound of Error (BOE) for a 90% Confidence interval of the difference of two proportions for voting for males compared with females? 

• 1.645* SORT[4.6171*3829/364+ (6171*3829)396] 

• 1.96* SORT[(61713829)/364 +(-61713829)396] 

• 1.645* SQRT[(-5962.4038)/364+(6364*3636)/396] 

• 1.96* SQRT{(.59622.4038/364+ (-6364 3636)/396]

3. The width of a confidence interval is influenced by which of the following

a. The variance of the population

b. The sample size

c. The level of the Confidence Coefficient

d. All of the answers are correct

Answer 1

1)

sample #1   ----->   male
first sample size,     n1=   364
number of successes, sample 1 =     x1=   217
proportion success of sample 1 , p̂1=   x1/n1=   0.5962
      
sample #2   ----->   female
second sample size,     n2 =    396
number of successes, sample 2 =     x2 =    252
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.6364

Std error , SE =    SQRT(p̂1 * (1 - p̂1)/n1 + p̂2 * (1-p̂2)/n2) =

so, answer: option A)

2)

level of significance, α =   0.10          
Z critical value =   Z α/2 =    1.645   [excel function: =normsinv(α/2)  
Bound of error , = Z*SE

so, answer: option C)

3)

d. All of the answers are correct