Question

Suppose a huge internet-based lighting company receives a shipment of several thousand boxes of light bulbs every Tuesday. Inspectors return the merchandise to the manufacturer if the proportion of damaged light bulbs is more than 0.06 (6%). Rather than inspect all of the packages, 100 boxes are randomly sampled. As long as at least 10 damaged and 10 undamaged light bulbs are found, a one-sample zz ‑test is run with a significance level of 0.05 to see if the proportion of damaged light bulbs in this shipment exceeds 0.06. The test has a power of 0.85 to correctly reject their null hypothesis if the proportion of damaged light bulbs exceeds 0.08. If the lighting company decides to return the shipment to the manufacturer, what is the probability that a type I error has been made? Give your answer as a decimal precise to two decimal places.

Answer 1

The probability of making a type I error is 0.05.

Step-by-step explanation:

To find the probability of a type I error, we need to first understand what a type I error is. In hypothesis testing, a type I error occurs when we reject the null hypothesis when it is actually true. In this case, the null hypothesis is that the proportion of damaged light bulbs in the shipment is not more than 0.06.

The significance level, also called alpha, is the probability of making a type I error. In this case, the significance level is given as 0.05. This means that if the null hypothesis is true, there is a 5% chance of mistakenly rejecting it.

Therefore, the probability of making a type I error in this scenario is 0.05.

Answer 2

Hello!

The Type I error means to reject the null hypothesis when the hypothesis is true. The probability asociated to this decision is the significance level of the test, symbolized α. For this problem, the probability of commiting a type I error (this means, rejecting the null hypothesis "the proportion of damaged light bulbs is less than 0.06" when the hypothesis is true) is 0.05.

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Step-by-step explanation: