A local newspaper in a large city wants to assess support for the construction of a highway bypass around the central business district to reduce downtown traffic. They survey a random sample of 1152 residents and find that 543 of them support the bypass. Construct and interpret a 95% confidence interval to estimate the proportion of residents who support construction of the bypass.

Question

A local newspaper in a large city wants to assess support for the construction of a highway bypass around the central business district to reduce downtown traffic.  They survey a random sample of 1152 residents and find that 543 of them support the bypass.  Construct and interpret a 95% confidence interval to estimate the proportion of residents who support construction of the bypass.

kriteria0b1 · Accepted Answer

given that,possible chances (x)=543size(n)=1152success rate ( p )= x/n = 0.4714point of estimate = proportion = 0.4714standard error    =                    (        0.4714        ⋅        0.5286        )            1152      = 0.0147margin of error   =  Z      a    2    ⋅  (standard error)where,   Z      a    2    =  Z-table valuelevel of significance,   α  =  0.05from standard normal table, two tailed   z      α    2    =  1.96  margin of error   =  1.96  ⋅  0.0147= 0.0288  C  I  =  [  p  ±   margin of error  ]  confidence interval   =  [  0.4714  ±  0.0288  ]  =  [  0.4425  ,  0.5002  ]