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.

Question

contestada

Respuesta :

KrystaCort KrystaCort · Answer 1 · 2019-10-18T08:55:51+02:00

Answer:

The result is significant.

Step-by-step explanation:

Here,

p = 30 ÷ 330 = 0.091

thus, q = 1 - p = 0.909

Also, [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 = 0.005

The result is significant at p < .05.