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.

Question

Mathematics

Sheldon Mcclain

22 January, 10:40

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.

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Sincere May · Answer 1

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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