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A fit is rolled 25 times and 12 evens are observed. Calculate and interpret a 95% confidence interval to estimate the true proportion of evens rolled on a die.

User Cheshire
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1 Answer

9 votes

Answer:

95% confidence interval to estimate the true proportion of evens rolled on a die.

(0.197368 , 0.762632)

Step-by-step explanation:

Step-by-step explanation:-

Given A fit is rolled 25 times and 12 evens are observed

proportion
p = (x)/(n) = (12)/(25) = 0.48

q = 1 - p = 1- 0.48 = 0.52

Level of significance =0.05


Z_(0.05) = 1.96

95% confidence interval to estimate the true proportion of evens rolled on a die.


(p^(-) - Z_(0.05) \sqrt{(p(1-p))/(n) } , p^(-) + Z_(0.05) \sqrt{(p(1-p))/(n) } )


(0.48 - 1.96 \sqrt{(0.48(1-0.48))/(12) } , 0.48 + 1.96 \sqrt{(0.48(1-0.48))/(12) } )

( 0.48 - 1.96 (0.1442 , 0.48 + 1.96(0.1442)

( 0.48 - 0.282632 , 0.48 + 0.282632)

(0.197368 , 0.762632)

Final answer:-

95% confidence interval to estimate the true proportion of evens rolled on a die.

(0.197368 , 0.762632)

User Egal
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