SOLUTION: 5. Mr. Sy asserts that fewer than 5% of the bulbs that he sells are defective. Suppose 300 bulbs are randomly selected, each tested and 10 defective bulbs are found. Does this prov

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Question 1186604: 5. Mr. Sy asserts that fewer than 5% of the bulbs that he sells are defective. Suppose 300 bulbs are randomly selected, each tested and 10 defective bulbs are found. Does this provide sufficient evidence for Mr Sy to conclude that the fraction of defective bulbs is less than 0.05? Use alpha 0.01 and the p- value approach.
answer the problem using the steps in hypothesis testing.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
H%5B0%5D%3A+p+=+0.05
H%5B1%5D%3A+p+%3C+0.05
The distribution of sample proportions will have a standard error of sqrt%28%28p%281-p%29%29%2Fn%29. We use the z-statistic to test the hypothesis.
The sample proportion obtained was %22p%27%22+=+10%2F300+=+1%2F30.
The level of significance is alpha+=+0.01.

, to 4 d.p. The p-value is P(z < -1.3245) = 0.093.

Since p-value > alpha = 0.01, the null hypothesis is not rejected, and we conclude that the percentage of defective bulbs is still at 5% (or maybe more).

*Normal probabilities were taken from https://stattrek.com/online-calculator/normal.aspx.