What is the Probability of Rejecting the Mean of 130 at the 1% Level?

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SUMMARY

The discussion focuses on calculating the probability of rejecting a null hypothesis that the mean voltage is 130 volts at a 1% significance level, given a sample mean of 128.25 volts from 20 readings with a standard deviation of 3. The critical value for the 1% level has already been determined, and the user is seeking clarification on the application of Bayesian methods in this context. The main conclusion is that the probability of rejecting the null hypothesis can be computed using the sample statistics provided.

PREREQUISITES
  • Understanding of hypothesis testing and significance levels
  • Familiarity with the concepts of sample mean and standard deviation
  • Knowledge of critical values in statistical tests
  • Basic understanding of Bayesian methods in statistics
NEXT STEPS
  • Calculate the probability of rejecting the null hypothesis using the Z-test
  • Explore the implications of using Bayesian methods for hypothesis testing
  • Review the concept of critical values and their determination
  • Study the relationship between sample size and hypothesis testing outcomes
USEFUL FOR

Students in statistics, data analysts, and anyone involved in hypothesis testing and statistical inference, particularly in the context of quality control and voltage measurements.

dim&dimmer
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Homework Statement


Having trouble understanding the question, which is...
voltage specified to be 130
Sample of 20 readings gives sample mean of 128.25
Also given s.d.=3.

"It is important that the voltage not be allowed to drop below 128 volts. What is the probability of rejecting mean of 130 at the 1% level if in fact the mean is 128?


Homework Equations


this is part c, already tested the hypothesis regarding the true mean and found the critical value for 1%.


The Attempt at a Solution


I think this involves bayesian methods but the language (grammar) of the question confuses me, if someone could restate it that would be great.
 
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