Question

A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.

	Better	Same	Worse	Totals
Republican	38	104	44	186
Democrat	12	87	137	236
Neither Party	21	90	118	229
Totals:	71	281	299	651

Express each of your first five answers as a decimal and round to the nearest 0.001 (in other words, type 0.123, not 12.3% or 0.123456).

What proportion of survey respondents identified themselves as Republicans?

What proportion of survey respondents thought the economy was getting worse?

What proportion of Republicans thought the economy was getting worse?

Among survey respondents who thought the economy was getting worse, what proportion were Republicans?

What proportion of survey respondents were Republicans who thought the economy was getting worse?

The three pie charts below show the opinions about the economy for each of party:

Democrats
36.9%58.1%gettingbetter5.1%about thesame36.9%gettingworse58.1%

Data	Percentage
getting better	0.051
about the same	0.369
getting worse	0.581

Republicans
20.4%23.7%55.9%gettingbetter20.4%about thesame55.9%gettingworse23.7%

Data	Percentage
getting better	0.204
about the same	0.559
getting worse	0.237

none
39.3%51.5%gettingbetter9.2%about thesame39.3%gettingworse51.5%

Data	Percentage
getting better	0.092
about the same	0.393
getting worse	0.515

Based on these pie charts, is there evidence that opinion about the economy is independent of party affiliation? Choose the statement below that best answers this question.

• There is evidence that opinion about the economy is independent of party affiliation.
• There is evidence that party affiliation depends on opinion about the economy.
• There is evidence that opinion about the economy is not independent of party affiliation.
• There is evidence that opinion about the economy depends on party affiliation.
• There is evidence that party affiliation and opinion about the economy are dependent.

Answer 1

A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.

                     better same worse Total

Republican. 38   104   44           186

Democrat        12     87. 137         236

Neither party   21   90    118.        229

Total.                71. 281. 299.      651

Solution :

Total number of survey respondents   = 651

1) Total number of survey respondents identified themselves as republicans = 186

Proportion of survey respondents identified themselves as republicans

= 186 / 651

= 0.2857

2) Number of survey respondents thought the economy was getting worse = 299

Proportion of survey respondents thought the economy was getting worse

= 299/ 651

= 0.4592

3) Total number of survey respondents identified themselves as republicans = 186

    Number of republicans thought economy was getting worse = 44  

Proportion of republicans thought economy was getting worse

= 44 / 186

= 0.2365

4) Number of survey respondents who thought the economy was getting worse = 299

   Number of survey respondents identified themselves as republicans and thought the economy was getting worse = 44

Proportion of survey respondents identify themselves as republican and thought the economy was getting worse

= 44 / 299

= 0.1472

5) Number of republicans thought the economy was getting worse = 44

Proportion of survey respondents were republicans who thought the economy was getting worse

   = 44 / 651

= 0.0675

From pie chart

Yes, There is evidence that party affiliation and opinion about the economy are independent.