Question

Out of 1210 people chosen at random, 277 of them said they approve of the job that Congress is doing.

Use a 95% confidence interval to estimate the approval rating for Congress.

Answer 1

Sol:

smpe proportion who told they approve of the job that Congress is doing=x/n=277/1210= 0.2289256

z crit for 95%=1.96

95% confidence interval for approve of the job that Congress is doing

p^-z*sqrt(p^*(1-p^)/n),p^+z*sqrt(p^*(1-p^/n)

0.2289256-1.96*sqrt(0.2289256*(1-0.2289256)/1210),0.2289256+1.96*sqrt(0.2289256*(1-0.2289256)/1210)

0.2052523, 0.2525989

95% lower limti for mean=0.2052523

95% upper limit for mean=0.2525989

we are 95% confidennt that the true ppopulation  approve of the job that Congress is doing.

lies in between 0.2052523 and  0.2525989