| Probabilities | P |
|---|---|
| one-tailed for —z | -- |
| one-tailed for +z | -- |
| two-tailed for ±z | -- |
| area between ±z | -- |
In literal terms, critical value is defined as any point present on a line which dissects the graph into two equal parts. The rejection or acceptance of null hypothesis depends on the region in which the value falls. The rejection region is defined as one of the two sections that are split by the critical value. If the test value is present in the rejection region, then the null hypothesis would not have any acceptance.
Two formulae can be used to determine the critical value. These are listed as follows.
1. \(\mathrm{Critical Value = \dfrac{Margin\ of\ Error} {Standard\ Deviation}}\)
2. \( \mathrm {Critical Value = \dfrac{Margin\ of\ Error} {Standard\ Error\ of\ Sample}} \)
Anyone of the two formulae listed above can be used to determine Critical Value depending on the known values.
Here are the steps you need to complete for calculating the critical value
This is the first step which the user has to complete for finding out the critical value. To determine the value of Alpha level, the following formula will be used.
\( \mathrm{Alpha\ Level} = 100% - \mathrm{Confidence Interval} \)
Consider that the confidence interval is 80%. Thus, Alpha Level will be given as.
\( \mathrm{Alpha\ Level} = 100 - 80 \)
\( \mathrm{Alpha\ Level} = 20% \)
The second step involves converting the value of alpha to decimal. By default, it has the percentage unit. Hence, convert it to the decimal format. In step, the value of alpha is 20%. Thus, in terms of decimals, it would be \(0.2\)
\( \alpha = 0.2 \)
In this step, the value of alpha determined in step 2 would be divided by \(2\). In the above example, the value of alpha is \(0.2\).
\( \textbf{Thus}, \dfrac{\alpha} {2} = \dfrac{0.2}{2} \)
\( \dfrac{\alpha}{2} = 0.1 \)
The value of α /2 = 0.1. In this step, subtract this value from 1.
\( \textbf{Thus}, 1 - \, 0.1 = 0.9 \)
Converting this decimal value to a percentage. Thus, 0.9 would be 90%. The corresponding critical value will be for a confidence interval of 90%. It would be given as:
\( \mathbf{Z = 1.645} \)
Note: To calculate t critical value, f critical value, r critical value, z critical value and chi-square critical use our advance critical values calculator. It helps to calculate the value from the Z table very quickly in real-time.
The common confidence levels and the corresponding critical values in the form of a table are given below.
| Confidence Level | Critical Value (Z-score) |
| 0.90 | 1.645 |
| 0.91 | 1.70 |
| 0.92 | 1.75 |
| 0.93 | 1.81 |
| 0.94 | 1.88 |
| 0.95 | 1.96 |
| 0.96 | 2.05 |
| 0.97 | 2.17 |
| 0.98 | 2.33 |
| 0.99 | 2.57 |
To get the null hypothesis, various methods are used to determine the required area. The common methods used include z tests, t scores and also chi tests. All these methods are used to determine null hypothesis. However, null hypothesis is the area between right and left tails. The right tail has positive values while the left tail has negative ones. This point is incorporated when the critical value has to be determined.
The standard normal model is used to determine the value of Z. The graphical display of normal distribution shows that the graph is divided into two main regions. The first one is called the Central Region and the other is the Tail Region.
\( \mathrm {Tail Value = 1 \space - \space Central Value} \)
This tool is actually very helpful for the determination of critical value. It cuts down the time needed to determine critical value. Other than that, it is very easy to use so users are able to calculate the correct results without any difficulties.
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