Critical Value Examples

t Critical Value Examples

Example 1

Evaluate the t critical value with the help of given values:

Significance level = 0.01

Number of samples = 25. 

Solution

Step 1: First of all, find the degree of freedom (Df) by taking the difference of 1 and the number of samples.

Df = 25 – 1

Df = 24

Step 2: Now take a one-tailed or two-tailed t-distribution table. Search the value of the degree of freedom in the leftmost column of the table. 

Step 3: Now choose the value of the significance level in the topmost row of the t table.

Step 4: To calculate the t critical value, get the value where both degrees of freedom and significance level intersect.

t critical value = 2.4851

Examples of z Critical Value

Example 1

Calculate the z critical value with the help of the given significance level.

Significance level = 0.06

Solution

Step 1: First of all, calculate half of the given significance level (α)

α/2 = 0.06/2 = 0.03

Step 2: Now subtract the above value from 1.

1 - α/2 = 1 – 0.03 = 0.97

Step 3: Now take a z distribution table and search the above value in the table.

Step 4: After indicating the value on the z distribution table, take its corresponding degree of freedom and significance level and add them.

Df = 1.8

Significance level = 0.08

z critical value = 1.8 + 0.08

z critical value = 1.88

Examples of p Critical Value

Example 1

Emma wants to check the p-value of an experiment of filling 250 boxes of mango juice according to the status 100ml. Calculate the p-value of the experiment if the z-value for one-tailed is 0.35

Solution

Step 1: First of all, make the null and alternative hypotheses of the given experiment.

Null hypothesis = h₀ = quantity of mango juice in the boxes is 100ml

Alternative hypothesis = h_a = quantity of mango juice in the boxes is different from 100ml

Step 2: Now find the test statistics of the given experiment according to the given values.

The test statistics of the given experiment are already given.

Z value = 0.35

Step 3: Now take a standard distribution table and indicate the corresponding value on that table.

The value on the standard distribution table is 0.36317

Note: If the test or z value is two-tailed then you have to multiply the corresponding value on standard distribution table by 2.