Statistical Significance: Manufacturer's Claim Rejected?

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SUMMARY

The discussion centers on evaluating the statistical significance of a manufacturer's claim regarding laptop defects. The manufacturer asserts that only 1% of their laptops are defective, but a sample of 600 laptops revealed a defect rate of 3%. Given that the probability of observing such a high defect rate under the manufacturer's claim is less than 0.1%, there is statistically significant evidence to reject the manufacturer's claim.

PREREQUISITES
  • Understanding of statistical significance and hypothesis testing
  • Familiarity with sampling methods and sample size implications
  • Knowledge of probability distributions, particularly binomial distribution
  • Basic comprehension of p-values and their interpretation
NEXT STEPS
  • Study the concept of p-values in hypothesis testing
  • Learn about the binomial distribution and its applications in quality control
  • Explore the implications of sample size on statistical power
  • Investigate common statistical tests used for proportion comparisons, such as the Chi-square test
USEFUL FOR

This discussion is beneficial for statisticians, quality assurance professionals, and anyone involved in product reliability analysis or evaluating claims based on statistical data.

rainbow1
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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"?
 

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