umthumaL3e

2022-12-03

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

Expert

given that,
possible chances (x)=543
size(n)=1152
success rate ( p )= x/n = 0.4714
point of estimate = proportion = 0.4714
standard error $=\sqrt{\frac{\left(0.4714\cdot 0.5286\right)}{1152}}$
= 0.0147
margin of error $=Z\frac{a}{2}\cdot \text{(standard error)}$
where,
$Z\frac{a}{2}=Z$-table value
level of significance, $\alpha =0.05$
from standard normal table, two tailed $z\frac{\alpha }{2}=1.96$

= 0.0288

$=\left[0.4425,0.5002\right]$

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