Question: A survey of 120 families showed that at least 78 had a computer at home. Find the 99% confidence interval of the true proportion of families who own a home computer. A ) 64.5% < p < 65.5% B ) 5.38% < p < 7.62% C ) 53.8% < p < 76.2% D ) 60.6% < p < 69.4% Steps to derive 1 The problem is to find the true proportion of families who own a home computer2 Sample proportion, p ˆ = 7 8 1 2 0 = 0.65 and q ˆ = 1 - p ˆ = 1 - 0.65 = 0.353 For 99% confidence interval, α = 1 - 0.99 = 0.01 and z ∝ /2 = 2.58 [Use the standard normal distribution table.]4 The 99% confidence interval for the true proportion is:p ˆ - z ∝ /2 p ˆ q ˆ n < p < p ˆ + z ∝ /2 p ˆ q ˆ n
[Formula.]5 0.65 - 2.58( 0 . 6 5 ) ( 0 . 3 5 ) 1 2 0 < p < 0.65 - 2.58( 0 . 6 5 ) ( 0 . 3 5 ) 1 2 0
6 0.65 - 0.112 < p < 0.65 + 0.112
7 0.538 < p < 0.762
8 53.8% < p < 76.2%
9 So, we are fairly 99% confident, that the families who own a home computer is between 53.8% and 76.2%.Hence the right answer is Option C Click Here To Go Back Few Other Questions - Use the change of base formula to evaluate log0.1 21... Solve for x.14 + 14(- x + 2) = 8x - 3(5 + x).. Use the change of base formula to evaluate log24 2... Find the property illustrated by the relation: |3.5s| + |11s| = |11s| + |3.5s|.. Use the change of base formula to evaluate log0.7 26... Use the change of base formula to evaluate log21 6... Use the change of base formula to evaluate log0.1 28... Use the change of base formula to evaluate log22 3... In the figure, PR = 52 cm, a = 2, b = 4 and c = 15. Find PQ... Use the change of base formula to evaluate log20 9... Use the change of base formula to evaluate log0.2 26... Use the change of base formula to evaluate log22 2... Solve for p.18 + 18(- p + 1) = 8p - 2(6 + p).. Use the change of base formula to evaluate log0.8 26... 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