Optimal Sample Size for Testing Raisin Content in Buns

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SUMMARY

The optimal sample size for testing the average number of raisins in buns, given a mean of 9 and a variance of 9, requires a minimum of 82 buns to achieve a significance level of 0.05 with 90% power. The formula used for calculating the sample size is n = (zα + zβ)² * σ² / δ², where zα and zβ correspond to the critical values for the significance level and power, respectively. The initial calculation of 78 buns was incorrect due to an underestimation of the required sample size.

PREREQUISITES
  • Understanding of statistical significance levels and power analysis
  • Familiarity with the concepts of z-scores in hypothesis testing
  • Knowledge of variance and its role in sample size calculations
  • Basic proficiency in using statistical formulas for sample size determination
NEXT STEPS
  • Study the calculation of sample sizes for different significance levels and power using statistical software
  • Learn about the implications of variance in sample size determination
  • Explore the use of z-scores in hypothesis testing and their derivation
  • Investigate the differences between z-tests and t-tests in sample size calculations
USEFUL FOR

Statisticians, researchers conducting experiments, and quality control analysts in food production who need to determine appropriate sample sizes for testing product content.

superwolf
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If the average number of raisins in a randomly chosen bun is 9 with a variance of 9, how many buns must be tested if a test with a significance level of 0.05 with 90% probability is going to reveal than the number of raisins is less than 10?

ATTEMPT:

[tex] n = \frac{(z_{\alpha} + z_{\beta})^2 \sigma^2}{\delta^2} = \frac{(1.645+1.28)^2 \cdot 9}{1^2} = 77.0006[/tex]

So, at least 78 buns.

Correct answer. At least 82 buns.

What's wrong?
 
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Help us out here. What test are you using? It looks vaguely like something to do with the F statistic, but I don't have my statistics references with me. What do z_alpha and z_beta represent, and how did you get them?
 

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