Question

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.

Answer 1

The result is significant.

Explanation:

Here,

p = 30 ÷ 330 = 0.091

thus, q = 1 - p = 0.909

Also,
`\sigma=\sqrt{(pq)/(n) }`

⇒
`\sigma=\sqrt{(0.091*0.909)/(330) }=0.0158`

The z-score is:

`z=(p-p_(0))/(\sigma)`

`z=(0.091-0.05)/(0.0158)=2.595`

Thus, at 95% confidence interval, p-value = 0.005

The result is significant at p < .05.