A random sample of 330 electronic components manufactured by a certain process are tested, and 30 are found to be defective. A device will be manufactured in which two of the components will be connected in series. The components function independently, and the device will function only if both components function. Let q be the probability that a device functions. Find a 95% confidence interval for q. Round the answers to three decimal places.
Accepted Solution
A:
Answer:The result is significant.Step-by-step explanation:Here, p = 30 ÷ 330 = 0.091thus, q = 1 - p = 0.909Also, [tex]\sigma=\sqrt{\frac{pq}{n} }[/tex]⇒ [tex]\sigma=\sqrt{\frac{0.091\times0.909}{330} }=0.0158 [/tex] The z-score is:[tex]z=\frac{p-p_{0}}{\sigma}[/tex][tex]z=\frac{0.091-0.05}{0.0158}=2.595[/tex]Thus, at 95% confidence interval, p-value = 0.005The result is significant at p < .05.