Question

1.       the county health department has concerns about the chlorine level at a local water park. the health department tests the water monday with readings of 4 mg out of 100 ml. on thursday when the water is tested, the health dept. gets readings of 5 mg out of 120 ml. assume that the samples are independent and that they have been randomly selected. construct a 90% confidence interval for the difference in the proportions of water samples on monday and thursday.

Answer 1

Sample proportion 1 = 4 / 100 = 0.04

Sample proportion 2 = 5 / 120 = 0.042

90% confidence interval for p1 - p2 is

(1 - 2) - Z * sqrt [ 1 (1 - 1) / n1 + 2 ( 1 - 2) / n2 ] < p1 - p2 < (1 - 2) + Z * sqrt [ 1 (1 - 1) / n1 + 2 ( 1 - ​2) / n2 ]

(0.04 - 0.042) - 1.645 * sqrt [ 0.04 * 0.96 / 100 + 0.042 * 0.958 / 120 ] < p1 - p2 <

(0.04 - 0.042) + 1.645 * sqrt [ 0.04 * 0.96 / 100 + 0.042 * 0.958 / 120 ]

-0.046 < p1 - p2 < 0.042

90% CI for p1 - p2 is ( -0.046 , 0.042 )