Critical Values Calculator A 05 N 18

This critical values calculator helps you find critical values for a significance level of 0.05 and a sample size of 18. Critical values are essential in hypothesis testing to determine whether to reject or fail to reject the null hypothesis.

What Are Critical Values?

Critical values are specific points on the distribution of a test statistic that help determine whether to reject the null hypothesis. They are derived from the sampling distribution of the test statistic under the assumption that the null hypothesis is true.

For a significance level (α) of 0.05 and a sample size (n) of 18, the critical values help you decide whether your test statistic is extreme enough to reject the null hypothesis.

Key Points

Critical values depend on the significance level (α) and the sample size (n).
They are used to set the rejection region for hypothesis tests.
Different distributions (e.g., t-distribution, z-distribution) have different critical values.

How to Use This Calculator

Using this critical values calculator is straightforward. Follow these steps:

Enter the significance level (α) in the first field. The default is 0.05.
Enter the sample size (n) in the second field. The default is 18.
Select the type of distribution (e.g., t-distribution, z-distribution).
Click the "Calculate" button to get the critical values.
Review the results and interpretation.

Critical Value = F^-1(1 - α/2, n-1)

Critical Values Table

The following table shows critical values for a significance level of 0.05 and sample sizes from 1 to 30.

Sample Size (n)	Critical Value (t)
1	12.706
2	4.303
3	3.182
4	2.776
5	2.571
6	2.447
7	2.365
8	2.306
9	2.262
10	2.228
11	2.201
12	2.179
13	2.160
14	2.145
15	2.131
16	2.120
17	2.110
18	2.101
19	2.093
20	2.086
21	2.080
22	2.074
23	2.069
24	2.064
25	2.060
26	2.056
27	2.052
28	2.048
29	2.045
30	2.042

How to Interpret Results

Interpreting critical values involves comparing your test statistic to the critical value. Here's how to do it:

Calculate your test statistic (e.g., t-statistic).
Compare it to the critical value from the table.
If the absolute value of your test statistic is greater than the critical value, reject the null hypothesis.
If the absolute value of your test statistic is less than the critical value, fail to reject the null hypothesis.

Example

Suppose you have a sample size of 18 and a significance level of 0.05. The critical value from the table is 2.101. If your calculated t-statistic is 2.5, you would reject the null hypothesis because 2.5 > 2.101.

FAQ

What is the difference between critical values and p-values?: Critical values are used to set the rejection region for hypothesis tests, while p-values indicate the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.
How do I choose the right distribution for critical values?: The choice of distribution depends on the type of data and the assumptions of your hypothesis test. Common distributions include the t-distribution, z-distribution, and chi-square distribution.
Can I use this calculator for one-tailed tests?: Yes, you can adjust the significance level (α) for one-tailed tests by using α/2 for two-tailed tests and α for one-tailed tests.
What if my sample size is larger than 30?: For large sample sizes, the critical values approach those of the normal distribution (z-distribution). You can use the z-distribution table for sample sizes greater than 30.
How accurate are the critical values provided by this calculator?: The critical values are calculated using standard statistical tables and formulas. For precise calculations, you may need to use specialized statistical software.