business statistics

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
Republican	38	104	44
Democrat	12	87	137
none	21	90	118

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 fraction of survey respondents identified themselves as Democrats? _____ In__correct

What fraction of survey respondents thought the economy was about the same? ______Correct

What fraction of Democrats thought the economy was about the same? _____

Among survey respondents who thought the economy was about the same, what fraction were Democrats? _____

What fraction of survey respondents were Democrats who thought the economy was about the same? _____

Answer 1

Hi Salma,

First question—add up total of all democrats, regardless of their opinion, and divide by total sample size 651:

P=(12 + 87 +137)/651= 0.363

Second Question—add up total of same column and divide by 651:

P=(104 + 87 +90)/651=0.432

Third Question—first add up total democrats.

Dems.=12 + 87 + 137= 236

Then look in the table for cell with “democrats” and “same.” This is 87. Now:

P=87/236=0.369

Fourth Question—same procedure in reverse. First add up total same respondents in column:

Same=104 + 87 + 90= 281

Then do the same as above—look for value in same and democrat cell; this is 87, so:

P=87/281=0.310

Final Question—We already found the cell for “same” and “democrats”. Again, that value is 87. Now, we are asked about the probability among ALL SURVEY RESPONDENTS that it is a democrat who believes the economy is the same, so that is:

P=87/651=0.134

I hope this helps.