Question

A U.S. Coast Guard survey of 300 small boats in the Cape Cod area found 120 in violation of one or more safety regulations. Give a 98% confidence interval (z*=2.326) for p, the proportion of all unsafe small boats. (Round your answer to 3 decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 120 / 300 = 0.4

Z_/2 = 2.326

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

= 2.326 * (((0.4 * 0.6) / 300)

= 0.066

A 98% confidence interval for population proportion p is ,

- E < p < + E

0.4 - 0.066 < p < 0.4 + 0.066

0.334 < p < 0.466

(0.334 , 0.466)