Chapter 10, Problem 30PT3

(a)

To determine

To check: Percentage of Republicans among the respondents is 41%.

Answer to Problem 30PT3

The statement is false.

Explanation of Solution

Given information:

The two way table of responses by political persuasion is as follows

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

Total number of respondents = 1850.

Formula used:

  $\text{Percentage of republicans}=\frac{Number\text{ of republicans}}{\text{Total number of respondents}}\times 100$

Calculation:

Number of republicans = 712

Percentage of republicans

  $=\frac{712}{1850}\times 100=38.486\%$

(b)

To determine

To check: Marginal distribution of choice of candidates

Answer to Problem 30PT3

The statement is true.

Explanation of Solution

Formula used:

Marginal distribution

Obama

  $\frac{Number\text{ of Obama choice}}{\text{Total number of respondents}}\times 100$

McCain

  $\frac{Number\text{ of McCain choice}}{\text{Total number of respondents}}\times 100$

Other

  $\frac{Number\text{ of Other choice}}{\text{Total number of respondents}}\times 100$

Undecided

  $\frac{Number\text{ of Undecided choice}}{\text{Total number of respondents}}\times 100$

Calculation:

Number of Obama choice respondents $=1029$

Marginal distribution of

Obama: $\frac{1029}{1850}\times 100=55.6\%$

Number of McCain choice respondents $=695$

Marginal distribution of

McCain: $\frac{695}{1850}\times 100=37.6\%$

Number of Other choice respondents $=21$

Marginal distribution of

Other: $\frac{21}{1850}\times 100=1.1\%$

Number of Undecided choice respondents $=105$

Marginal distribution of

Undecided: $\frac{105}{1850}\times 100=5.7\%$

(c)

To determine

To check: Percentage of democrats planned to vote for McCain is $11.2\%$ .

Answer to Problem 30PT3

The statement is false.

Explanation of Solution

Formula used:

  $\frac{Number\text{ of democrats voted McCain}}{Number\text{ of Democrats}}\times 100$

Calculation:

Number of democrats $=1037$

Number of democrats voted McCain $=78$

The required percentage is $\frac{78}{1037}\times 100=7.52\%$

(d)

To determine

To check: Percentage of those undecidedare Independents is $44.6\%$ .

Answer to Problem 30PT3

Explanation of Solution

Formula used:

  $\frac{Number\text{ of undecided and Independents}}{Number\text{ of undecided}}\times 100$

Calculation:

Number of undecided $=105$

Number of respondents undecided and Independent $=45$

The required percentage is $\frac{45}{105}\times 100=42.9\%$

(e)

To determine

To check: The conditional distribution of political persuasion given McCain is the choice is Democrats: $7.5\%$ , Republicans: $84.0\%$ , Independent: $18.8\%$

Answer to Problem 30PT3

The statement is false.

Explanation of Solution

Formula used:

Democrat

  $\frac{Number\text{ of democrats voted McCain}}{Number\text{ of McCain}}\times 100$

Republican

  $\frac{Number\text{ of Republican voted McCain}}{Number\text{ of McCain}}\times 100$

Independent

  $\frac{Number\text{ of Independent voted McCain}}{Number\text{ of McCain}}\times 100$

Calculation:

Number of McCain respondents $=695$

Condition distribution of

Democrats

Number of democrats voted McCain $=78$

The required percentage is $\frac{78}{695}\times 100=11.2\%$

Republican

Number of Republican voted McCain $=598$

The required percentage is $\frac{598}{695}\times 100=86.0\%$

Independent

Number of Independent voted McCain $=19$

The required percentage is $\frac{19}{695}\times 100=2.8\%$