Question

Shortly before the $2012$presidential election, a survey was taken by the school newspaper at a very large state university. Randomly selected students were asked, “Whom do you plan to vote for in the upcoming presidential election?” Here is a two-way table of the responses by political persuasion for $1850$students:

Candidate of choice	Political persuasion
		Democrat	Republican	Independent	Total
	Obama	$925$	$78$	$26$	$1029$
	Romney	$78$	$598$	$19$	$695$
	Other	$2$	$8$	$11$	$21$
	Undecided	$32$	$28$	$45$	$105$
	Total	$1037$	$712$	$101$	$1850$

Which of the following statements about these data is true?

a. The percent of Republicans among the respondents is $41\%.$

b. The marginal relative frequencies for the variable choice of candidate are given by

Obama: $55.6\%$; Romney: $37.6\%$; Other: $1.1\%$; Undecided: $5.7\%$.

c. About $11.2\%$of Democrats reported that they planned to vote for Romney.

d. About $44.6\%$of those who are undecided are Independents.

e. The distribution of political persuasion among those for whom Romney is the

candidate of choice is Democrat: $7.5\%$; Republican: $84.0\%$; Independent: $18.8\%$.

Short answer

Option (b) is correct :

The marginal relative frequencies for the variable choice of candidate are given by

Obama: $55.6\%$; Romney: $37.6\%$; Other:$1.1\%$ ; Undecided: $5.7\%$.

Step-by-step solution

Given Information

We are given following table:

Candidate of choice	Political persuasion
		Democrat	Republican	Independent	Total
	Obama	$925$	$78$	$26$	$1029$
	Romney	$78$	$598$	$19$	$695$
	Other	$2$	$8$	$11$	$21$
	Undecided	$32$	$28$	$45$	$105$
	Total	$1037$	$712$	$101$	$1850$

We need to find correct alternative corresponding to given data.

Explanation

Formula for percentage = $\frac{value}{totalvalue}\times 100$

$\Rightarrow$Percentage of students who voted Republican = $\frac{712}{1850}\times 100=38\%$

So, option (a) is incorrect

$\Rightarrow$The marginal relative frequencies for the variable choice of candidate are given by

Obama = $\frac{1029}{1850}\times 100=55.6\%$ ; Romney = $\frac{695}{1850}\times 100=37.56\%$

Other = localid="1654225534579" $\frac{21}{1850}\times 100=1.1\%$; Undecided = localid="1654225615414" $\frac{105}{1850}\times 100=5.7\%$

So, option (b) is correct.

localid="1654225660667" $\Rightarrow$Percentage of democrats planned to vote for Romney = localid="1654225544682" $\frac{78}{1037}\times 100=7.5\%$

So, option (c) is incorrect.

localid="1654225663739" $\Rightarrow$Percentage of who are undecided are Independents = localid="1654225550676" $\frac{45}{106}\times 100=42.4\%$

So, option (d) is incorrect.

localid="1654225648597" $\Rightarrow$Percentage distribution of political persuasion among those for whom Romney =

Democrats supporting Romney = localid="1654225556232" $\frac{78}{1037}\times 100=7.5\%$

Republican supporting Romney = localid="1654225561219" $\frac{512}{598}\times 100=85.6\%$

So , option (e) is incorrect.

Hence, option (b) is the only correct option.