Question

A hat contains 10,000 balls. A random sample of 100 balls is selected from the hat....

A hat contains 10,000 balls. A random sample of 100 balls is selected from the hat. 17 of the selected balls are red, 27 are green and 56 are black. Construct a 96% confidence interval estimate for the percentage of green balls in the hat.

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Answer #1

Sample proportion for green balls = = 27/100 = 0.27

96% confidence interval for p is

- Z/2 * sqrt ( ( 1 - ) / n ) < p < + Z/2 * sqrt ( ( 1 - ) / n )

0.27 - 2.0537 * sqrt( 0.27 * 0.73 / 100) < p < 0.27 + 2.0537 * sqrt( 0.27 * 0.73 / 100)

0.179 < p < 0.361

96% CI is (0.179 , 0.361) = (17.9 , 36.1) %

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