Question

Shortly before the$2008$ 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:

Which of the following statements about these data is true?

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

(b) The marginal distribution of the variable choice of candidate is given by Obama: $55.6\%$; McCain: $37.6\%$; Other:$1.1\%$; Undecided: $5.7\%$.

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

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

(e) The conditional distribution of political persuasion among those for whom McCain is the candidate of choice is Democrat: $7.5\%$; Republican: $84.0\%$; Independent $18.8\%$:

Short answer

The correct answer is (d) and (b) (This can be found by taking each row total and dividing by the grand total.)

Step-by-step solution

Given information

We have been given that

Total Republican $=712$

Total respondents $=1850$

and we have to find out that which statement is true.

Explanation

Now, we will check all the options,

$1$. As the percentage of republicans is Total republican divided by sample total:

$\frac{712}{1850}=38\%$So,(a) is not correct option.

2. Now as the answer is satisfied so b is the correct option.

$3.$percentage of People planned to vote for McCain is $\frac{78}{1037}=7.5\%$so, option c is not correct.

$4.$As the percentage of people who are independents are $\frac{45}{101}=44.6\%$So, option d is correct.

$5.$The conditional distribution for democrats is $\frac{78}{695}=11.2\%$so, option e is not correct.

Hence, option b and d are correct.