Question

2. We refer to a recent poll on Democratic candidates for the Presidential election 2020, among a random national sample of 1,003 adults. Results have an error margin of plus or minus 3.5 percentage points. In the poll, Joe Biden, Elizabeth Warren, and Bernie Sanders were answered to be an appropriate candidate by 27%, 21%, and 19%, respectively. Assume the level of significance, α = 5%.

(a) Calculate the standard deviation of the sample. (25 pts)

(b) Evaluate the result on whether either the result of Biden or Sanders could be switched with Warren’s due to the margin of error. (25 pts)

Confidence Interval (50 pts) 2. We refer to a recent poll on Democratic candidates for the Presidential election 2020, among a random national sample of 1,003 adults. Results have an error margin of plus or minus 3.5 percentage points. In the poll, Joe Biden, Elizabeth Warren, and Bernie Sanders were answered to be an appropriate candidate by 27%, 21%, and 19%, respectively. Assume the level of significance, a = 5%. (a) Calculate the standard deviation of the sample. (25 pts) Note: Convert the results given in percentage points to the corresponding number of samples. (b) Evaluate the result on whether either the result of Biden or Sanders could be switched with Warren's due to the margin of error. (25 pts) ||

Answer 1

Answer:

Given the

We refer to a recent poll on Democratic candidates for the presindential election 2020

A random national sample of 1003 adults

An error margin of plus or minus 3.5 percentage points

in the pole , Joe Biden, Elizabeth waren, and Bernie Sanders were answered to be an appropriate candidate by 277., 214. and 1944. respectively. Assume the level of significance , a = st. a) The standard deviation of the sample. marginal enor = 3.5t. Standard eno : 3.5 2 score for a 3,5 20.5 So 3.5105 1645 So = 2.133 Also number of Sampley -274.+216 +94. standard . : 671. X100) · 672.01 deviation standard enci * (sample So. 2.184612.01 - 2.134 X25.923 So e 55.32

(6 we know that confidence interval using percent p 2 and margin of enor e can be given as (1-(P-E, Pte) In order to answer this question, we need to find the confidence interval for each candidate. - CE Biden = (P-E, ptt) +(27-3,5,2743.5) :- (23.5, 30.5) Ciwaneo - PE, P+E) → - (21-35 , 21 +3,5) : (175, 245 1 CI Sanders = (P-E, P+E) - 09-3.519+3,5) - (15,5; 22.5) Confidence interval for Biden is verlapping with waren's confidence Sanders is also overlapping Nal and confidence intertal for with waren's confidence interval. This mean that the results easily switched with waren of Biden and sonders can be due to margin of enor.