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 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?

A. 1.96 * SQRT[(.6171*.3829)/364 + (.6171*.3829)396]

B. 1.645 * SQRT[(.5962*.4038)/364+ (.6364*.3636)/396]

C. 1.96 * SQRT[(.5962*.4038)/364+ (.6364*.3636)/396]

D. 1.645 * SQRT[(.6171*.3829)/364 + (.6171*.3829)396]

Explanation / Answer

Gender Voted not voted

Total Males 217 147 364

Females 252 144 396

Total 399 361 760

from the table number of males voted = 217/364=0.5962 = p1

males not voted = 147/364=0.4038= q1

number of females voted from table = 252/396=0.6364 = p2

females not voted = 144/396 = 0.3636=q2

number of males n1 = 364

number of females n2 = 396

90% confidence interval standard z crtical value from strandard z table is Zcrit =1.645

bound of error or margin of error is given by

Zcrit*sqrt([p1q1/n1] +[p2q1/n2])

substuting above values in the given formules

1.645 * SQRT[(.5962*.4038)/364+ (.6364*.3636)/396]

so answer is option b

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