Answer: B. 0.4542 to 0.5105.
Step-by-step explanation:
The confidence interval for population proportion is given by :-
[tex]\hat{p}\pm z^* \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
, where [tex]\hat{p}[/tex] = Sample proportion.
n= sample size.
z* = Critical value.
Let p represent the proportion of residents in the community that support the property tax levy.
As per given , we have
Of the 850 residents surveyed, 410 supported the property tax levy.
i.e. n= 850 , [tex]\hat{p}=\dfrac{410}{850}=0.48235[/tex]
From z-table , the critical value corresponds to 90% confidence level = z*=1.645
Now, 90% confidence interval for p:
[tex]=0.48235\pm (1.645)\sqrt{\dfrac{0.48235(1-0.48235)}{850}}[/tex]
[tex]=0.48235\pm (1.645)\sqrt{0.00029375115}[/tex]
[tex]=0.48235\pm (1.645)(0.017139170049)[/tex]
[tex]=0.48235\pm 0.0281939[/tex]
[tex]=(0.48235-0.0281939,\ 0.48235+ 0.0281939)\\\\=(0.4541561,\ 0.5105439)\\\\\approx(0.4542,\ 0.5105)[/tex]
Hence, the correct answer is B. 0.4542 to 0.5105.
