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A survey finds that 55 people out of 170 favor increasing property taxes to help pay for a new library. If this data is used to estimate the population proportion who favor new taxes, the standard error of the estimate is:

A. 0.425

B. 0.036

C. 0.324

D. 0.001

E. 0.119

Respuesta :

JeanaShupp

Answer: B. 0.036

Step-by-step explanation:

Formula for standard error :

[tex]SE=\sqrt{\dfrac{p(1-p)}{n}}[/tex]

, where p = Population proportion and n= sample size.

Let p be the population proportion of the people who favor new taxes.

As per given , we have

n= 170

[tex]p=\dfrac{55}{170}\approx0.324[/tex]

Substitute these values in the formula, we get

[tex]SE=\sqrt{\dfrac{0.324(1-0.324)}{170}}\\\\=\sqrt{0.00129}\\\\=0.0359165699921\approx0.036[/tex]

Hence, the standard error of the estimate is 0.036.

∴ The correct answer is OPTION B. 0.036

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