Question

Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 248 with 120 successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.

_________< p <__________

Solution :

Given that,

Point estimate = sample proportion = = x / n = 120 / 248 = 0.484

1 - = 1 - 0.484 = 0..516

Z/2 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 * (((0.484 * 0.516) / 248)

= 0.052

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.484 - 0.052 < p < 0.484 + 0.052

0.432 < p < 0.536

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