Citizen registration and voting varies by age and gender. The following data is

Question

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 registered to vote for ages 18 to 24 compared with those 25 to 34. The expectation is that registration is lower for the younger age group. The data are given below. Age Registered Not Registered Total

18to 24 52 45 97

25 to 34 83 42 125

35 to 44 86 35 121

45 to 54 104 37 141

55 to 64 100 29 129

65 to 74 66 17 83

75 and over 50 13 63 Total 541 218 759

What is the Bound of Error (BOE) for a 95% Confidence Interval of the difference of two proportions for voter registration for persons 18 to 24 compared with 25 to 34?

1.96 * SQRT[(.6081*.3919)/97 + (.6081*.3919)125]

1.96 * SQRT[(.5361*.4639)/97 + (.6640*.3360)/125]

1.645 * SQRT[(.6081*.3919)/97 + (.6081*.3919)125]

1.645 * SQRT[(.5361*.4639)/97 + (.6640*.3360)/125]

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

A. SQRT[(.6081*.3919)/97 + (.6081*.3919)125]

B. SQRT[(.4987)/97 + (.4723)/125]

C. .0661

D. SQRT[(.5361*.4639)/97 + (.6640*.3360)/125]

1.96 * SQRT[(.6081*.3919)/97 + (.6081*.3919)125]

1.96 * SQRT[(.5361*.4639)/97 + (.6640*.3360)/125]

1.645 * SQRT[(.6081*.3919)/97 + (.6081*.3919)125]

1.645 * SQRT[(.5361*.4639)/97 + (.6640*.3360)/125]

Explanation / Answer

p1 = Proportion of registered voters among 18 to 24 = 52/97 = 0.5361

q1 = 1 - p1 = 1 - 0.5361 = 0.4639

p2 = Proportion of registered voters among 25 to 34 = 83/125 = 0.6640

q2 = 1 - p2 = 1 - 0.6640 = 0.3360

Hence,

Bound of error for 95% confidence interval:

1.96 * SQRT[(.5361*.4639)/97 + (.6640*.3360)/125]

Option B is correct.

Standard error:

SQRT[(.5361*.4639)/97 + (.6640*.3360)/125]

Option D is correct.

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