Question

If n=440 and ˆpp^ (p-hat) =0.75, find the margin of error at a
99% confidence level.

As in the reading, in your calculations:

--Use z = 1.645 for a 90% confidence interval

--Use z = 2 for a 95% confidence interval

--Use z = 2.576 for a 99% confidence interval.

Give your answer rounded to three decimal places.

Answer #1

**Solution = **

Given,

n = 440 ....... Sample size

= 0.75

Our aim is to construct 99% confidence interval.

c = 0.99

= 1 - c = 1- 0.99 = 0.01

/2 = 0.005 and 1- /2 = 0.995

Search the probability 0.995 in the Z table and see corresponding z value

= 2.576

Now , the margin of error is given by

E = /2 *

= 2.576 * [ 0.75 *(1 - 0.75)/ 440]

= 0.053

**Answer :**

**The margin of error is 0.053**

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