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Sagot :
Answer:
95% of the confidence interval for q is
(0.05809 , 0.1183)
Step-by-step explanation:
Step:1
Given that the random sample of 340 electronic components manufactured by a certain process is tested, and 30 are found to be defective.
sample proportion
[tex]q^{-} = \frac{x}{n} = \frac{30}{340} = 0.0882[/tex]
Step:2
95% of the confidence interval is determined by
[tex](q - Z_{0.05} \sqrt{\frac{pq}{n} } , q + Z_{0.05} \sqrt{\frac{pq}{n} } )[/tex]
[tex]((0.0804 -1.96 \sqrt{\frac{0.0804 X0.9118}{340} } ,0.0804 +1.96 \sqrt{\frac{0.0804 X0.9118}{340})[/tex]
[tex]( 0.0882- 1.96 \sqrt{0.000236} , 0.0882 + 1.96 \sqrt{0.000236} )[/tex]
(0.0882 - 0.03011 , 0.0882+0.03011)
( 0.05809 , 0.1183)
Final answer:-
95% of the confidence interval for q is
(0.05809 , 0.1183)
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