Question

A poll reported that only

482482

out of a total of

17901790

adults in a particular region said they had a​ "great deal of​ confidence" or​ "quite a lot of​ confidence" in the public school system. This was down 5 percentage points from the previous year. Assume the conditions for using the CLT are met. Complete parts​ (a) through​ (d) below.

a. Find a

9595​%

confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public​ schools, and interpret this interval.The

9595​%

confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the public schools is

Answer 1

Level of Significance,α = 0.05   

Number of Items of Interest,x =482

Sample Size,n = 1790

  

Sample Proportion , p̂ = x/n = 0.269

z -value =Zα/2 = 1.960                 [excel formula =NORMSINV(α/2)]

  

Standard Error , SE = √[p̂(1-p̂)/n] = 0.0105

margin of error , E = Z*SE = 1.960*0.0105=0.0205

  

95%Confidence Interval is

Interval Lower Limit = p̂ - E = 0.269-0.0205=0.2487

Interval Upper Limit = p̂ + E =0.269+0.0205=0.2898

  

95% confidence interval is (0.249< p < 0.290)