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

In summary, the problem involves determining the probability of rejecting a mean of 130 at a 1% level, given a sample mean of 128.25 and a standard deviation of 3. The question also mentions previously testing a hypothesis for the true mean and finding the critical value for 1%. The focus is on ensuring the voltage does not drop below 128 volts.
  • #1
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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  • #2
I have figured it out
 

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

What is a hypothesis test?

A hypothesis test is a statistical method used to determine whether a specific hypothesis about a population is supported by the data. It involves formulating a null hypothesis, which states that there is no significant difference between the observed data and the expected results, and an alternative hypothesis, which states that there is a significant difference.

What is a normal distribution?

A normal distribution is a common probability distribution that follows a bell-shaped curve. It is characterized by its mean, which is the central value of the distribution, and its standard deviation, which measures the spread of the data around the mean. Many natural phenomena, such as height and weight, follow a normal distribution.

Why is it important to use a normal distribution in hypothesis testing?

When conducting a hypothesis test, it is important to use a normal distribution because it allows for accurate and reliable statistical analysis. The central limit theorem states that the means of a large sample of independent and identically distributed random variables will be approximately normally distributed, regardless of the distribution of the individual variables. This makes the normal distribution a useful tool for hypothesis testing.

What is a p-value?

A p-value is the probability of obtaining results at least as extreme as the observed data, assuming that the null hypothesis is true. It is used in hypothesis testing to determine the significance of the results. A low p-value (usually less than 0.05) indicates that the observed results are unlikely to occur by chance and supports rejecting the null hypothesis in favor of the alternative hypothesis.

What is the significance level in hypothesis testing?

The significance level, also known as alpha, is the threshold used to determine whether the p-value is low enough to reject the null hypothesis. It is typically set at 0.05, meaning that there is a 5% chance of obtaining results as extreme as the observed data if the null hypothesis is true. A lower significance level leads to a more conservative approach, while a higher significance level may increase the likelihood of falsely rejecting the null hypothesis.

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