Statistics- Find Critical Value(s); Bell-Shaped Curve

In summary, the conversation discusses finding the critical value for different alpha levels (0.05, 0.01, and 0.005) in various types of tests (two-tailed, left-tailed, and right-tailed). The person seeking help is unsure of how to solve these questions and has tried researching but has not found a suitable solution. They also mention that alpha is not the standard deviation, but rather a measure of error or probability.
  • #1
oddjobmj
306
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Homework Statement


Find the critical value (or values) for the following and illustrate each using the Bell-Shaped Curve:

Numerous example such as-

1) [tex]\alpha[/tex] = 0.05, two-tailed test
2) [tex]\alpha[/tex] = 0.01, left-tailed test
3) [tex]\alpha[/tex] = 0.005, right-tailed test

Homework Equations



This is what I'm looking for. I believe the solution will be rather simple once I have some context but I was absent and am not sure where to look for how to solve these questions. Unfortunately my book doesn't have a glossary and I've re-read the chapters we were supposed to be going through to no avail. Google is yielding many results but none of which are using a variable [tex]\alpha[/tex] and because there are many different types of tests I can't figure out which one I'm supposed to use.

Thank you for your time,
Odd

EDIT:
I believe, in this case, a (alpha) stands for standard deviation. However, I'm still not sure what the standard setup of this problem would be since I'm -only- given a. Nothing more.
 
Last edited:
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  • #2
α (alpha) is not the standard deviation. It is the "alpha-level", or "probability of error level", or "p-value". Does this help?
 

Related to Statistics- Find Critical Value(s); Bell-Shaped Curve

1. What is a critical value in statistics?

A critical value in statistics is a value that is used to determine the rejection or acceptance of a null hypothesis in a hypothesis test. It is typically based on a significance level, which represents the probability of making a Type I error (incorrectly rejecting a true null hypothesis).

2. How do you find the critical value for a specific significance level?

The critical value for a specific significance level can be found using a critical value table or a statistical software program. The value is determined by the degrees of freedom and the desired significance level. For example, in a t-test with 10 degrees of freedom and a significance level of 0.05, the critical value would be 2.228.

3. What is the relationship between critical values and p-values?

The critical value is the threshold for determining whether a p-value is statistically significant or not. If the calculated p-value is less than the critical value, it is considered statistically significant and the null hypothesis can be rejected. If the p-value is greater than the critical value, it is not considered statistically significant and the null hypothesis cannot be rejected.

4. How is a bell-shaped curve related to critical values?

A bell-shaped curve, also known as a normal distribution, is a symmetrical probability distribution that is often used in statistical analysis. The critical values for a normal distribution can be found by dividing the desired significance level by two and finding the corresponding z-score on the standard normal distribution table.

5. Can critical values be used for any type of statistical test?

Yes, critical values can be used for any type of statistical test that involves hypothesis testing, such as t-tests, ANOVAs, and chi-square tests. However, the specific critical value used may vary depending on the type of test and the number of groups or variables being compared.

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