ework Assignment 8 KQuestion 7 (of 10) value 10.00 points A random sample of 50
ID: 3309313 • Letter: E
Question
ework Assignment 8 KQuestion 7 (of 10) value 10.00 points A random sample of 50 observations results in 40 successes. Use Table 1 a. Construct the a 99% confidence interval for the population proportion of successes (Round intermediate calculations to 4 decimal places. Round "z-value" and final answers to 3 decimal places.) Confidence interval to b. Construct the a 99% confidence interval for the population proportion of failures (Round intermediate calculations to 4 decimal places. Round "z-value and final answers to 3 decimal places.) Confidence interval to Hints eBook&Resources;
Explanation / Answer
Solution:- given that n = 50 , x = 40 , p = x/n = 40/50 = 0.8 , q = 1-p = 0.2
=> 99% confidence interval for the population proportion of successes
p +- Z * sqrt(pq/n)
=> (0.8 - 2.575 * sqrt((0.8*0.2)/50) , 0.8 + 2.575 * sqrt((0.8*0.2)/50) )
= ( 0.654 , 0.946)
=> 99% confidence interval for the population proportion of failures
q +- Z * sqrt(pq/n)
=> (0.2 - 2.575 * sqrt((0.8*0.2)/50) , 0.2 + 2.575 * sqrt((0.8*0.2)/50) )
= ( 0.054 , 0.346 )
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