MHB Statistical Significance: Manufacturer's Claim Rejected?

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The discussion centers on evaluating the statistical significance of a manufacturer's claim that only 1% of their laptops are defective, in light of a sample showing 3% defects. The evidence suggests that obtaining a sample defect rate of 3% would occur with less than a 0.1% probability if the true defect rate were indeed 1%. This low probability indicates that the observed defect rate is unlikely to be due to random chance. Therefore, there is statistically significant evidence against the manufacturer's claim of a 1% defect rate. The conclusion drawn is that the sample results provide strong grounds to question the accuracy of the manufacturer's assertion.
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form a conclusion about statistical significance. Do not make any formal calculations. Either use the results provided or make subjective judgments about the results.

a manufacturer of laptop computers claims that only 1% of their computers are defective. In a sample of 600 computers, it was found that 3% were defective. If the proportion of defectives were really only 1%, there would be less than 1 chance in 1000 of getting such a large proportion of defective laptops in the sample. Is there statistically significant evidence against the manufacturer's claim ? Why or why not?
 
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"If the proportion of defectives were really only 1%, there would be less than 1 chance in 1000 of getting such a large proportion of defective laptops in the sample. "

So what do you think? Is getting a result that is so unlikely to happen by chance "statistically significant"?
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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