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

69%

Explanation:

got it right

Answer 2

The percentage is between 66% to 90%

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(s)/(√(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.