Question

Calculate a 95 percent confidence interval for the proportion of interest. Make sure you check all conditions. (high interval) 0.397 and (low interval) 0.257 How do you do the success-failure condition for number 5? (when checking to see if all conditions are met).

Answer 1

We need to find the sample size n and .

The sample size is found to be 170 and = 0.327, as shown below.

(a) To check the condition if n * is > 10 and n * (1 - ) > 10 (Success failure condition)

n * = 170 * 0.327 = 55.59 which is > 10 and

n * (1 - ) = 170 * 0.673 = 114.41 which is > 10

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To find the sample size n and

The Upper Limit: 0.397 = + 1.96 * SE ---- (1)

The Lower Limit: 0.257 = - 1.96 * SE ----- (2)

Adding, 2 * = 0.654

Therefore = 0.327

Substituting in equation (1), we get 0.397 = 0.327 + 1.96 * SE

1.96 * SE = 0.397 - 0.327 = 0.07

Therefore SE = 0.07 / 1.96 = 0.036

SE =

0.036 =

Therefore squaring and cross multiplying,