Question

For a recent report on sleep deprivation, the Centers for Disease Control and Prevention interviewed 11545 residents of California and 4745 residents of Oregon. In California, 947 respondents reported getting insufficient rest or sleep during each of the preceding 30 days, while 408 of the respondents from Oregon reported the same. Calculate a 90 % confidence interval for the difference between the proportions of Californians and Oregonians, p California − p Oregon pCalifornia−pOregon , who report getting insufficient rest. Round your answer to 4 decimal places.

Answer 1

= 947 / 11545 = 0.0820, 1 - = 0.9180, n₁ = 11545,

= 408 / 4745 = 0.086 1 - = 0.914, n₂ = 4745,

The Zcritical (2 tail) for = 0.10, is 1.645

The Confidence Interval is given by (- ) ME, where

(- ) = 0.082 – 0.086 = -0.004

The Lower Limit = -0.004 - 0.0079 = - 0.0119

The Upper Limit = -0.004 + 0.0079 = 0.0039

The Confidence Interval is (-0.0119 , 0.0039)

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