Interpolation methods are used to estimate heights above sea

Interpolation methods are used to estimate heights above sea level for locations where direct measurements are unavailable. In an article, a weighted-average method of interpolation for estimating heights from GPS measurements is evaluated. The method made \"large\" errors (errors whose magnitude was above a commonly accepted threshold) at 25 of the 70 sample test locations. Find a 99% confidence interval for the proportion of locations at which this method will make large errors. Carry three significant digits throughout your calculations.

The 99% confidence interval is (, ).

Solution

CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=25
Sample Size(n)=70
Sample proportion = x/n =0.357
Confidence Interval = [ 0.357 ±Z a/2 ( Sqrt ( 0.357*0.643) /70)]
= [ 0.357 - 2.58* Sqrt(0.003) , 0.357 + 2.58* Sqrt(0.003) ]
= [ 0.209,0.505]