Question

A CNN poll was conducted from May 7 to May 10.  Among a random sample of 1001 registered voters, 511 of them supported Joe Biden. 503 out of these 1001 registered voters are democrats, and 87% of these 503 democrats supported Biden. Will the margin of error among democrats be greater than, less than, or equal to, that from all parties?  Explain

Answer 1

Given

A CNN poll was conducted from May 7 to May 10.

Size of random sample = 1001 registered voters

No. of people supporting Joe Biden = 511 out of 1001 registered voters

No. of democrats voters = 503 out of 1001 registered voters

Percentage of democrats who supported Biden = 87% out of 503 democrats

Now we have to calculate the margin of error amonng the democrats

Level of Significance, α = 0.05

Number of Items of Interest, x = 503 x 87% = 437.61

Sample Size, n = 503

From the z-tables at significance level = 0.025, the z-value is 1.96

Therefore,

z-value= 1.96

Now we have to calculate the margin of error amonng the parties

Level of Significance, α = 0.05

Number of Items of Interest, x = 503

Sample Size, n = 1001

From the z-tables at significance level = 0.025, the z-value is 1.96

Therefore,

z-value= 1.96

From the both margin of error values we can conclude that the margin of error for democrats is less than the parties.