Question

suppose a study estimated that 78% of the residents of a town (with an error range plus/minus12 percentage points at 95% confidence) favor building a new community center. which of the following percentages of the towns residents may favor building a new community center

Answer 1

Answer:

The percentage is between 66% to 90%

Step-by-step explanation:

Confidence Interval-

A confidence interval is the range of values we are fairly sure the true value will lie in that range or interval.

Mathematically, the range of confidence interval of a sample is,

$=\text{Average}\pm \text{Margin of error}$

                                 or

$=\overline X\pm Z\dfrac{s}{\sqrt{n}}$

where,

$\overline X$ = is the mean

Z = Z-value of confidence interval

s = standard deviation

n = number of observations

Putting the values, confidence interval will be,

$=78\pm 12\\\\=66\%\ to\ 90\%$

Therefore, any percentage value in between 66% to 90% will be the percentages of the towns residents who may favor building a new community center.

Answer 2

the Answer is 69% -Apex