# Use the student t table to find the following values: (a) t_{0.05,20};(b) t_{0.10,10};(c)...

## Question:

Use the student t table to find the following values:

{eq}(a) t_{0.05,20};(b) t_{0.10,10};(c) t_{0.025,13};(d) t_{0.025,200};(e) t_{0.05,95} {/eq}

Use the {eq}\chi^2 {/eq} table to find the following values of {eq}\chi^2: {/eq}

{eq}(a) \chi^2_{0.10,5};(b) \chi^2_{0.01,100};(c) \chi^2_{0.95,18};(d) \chi^2_{0.99,60} {/eq}

Use the F table to find the following values of F:

{eq}(a) F_{0.05,3,7};(b) F_{0.05,7,3};(c) F_{0.025,5,20};(d) F_{0.01,12,60} {/eq}

## Determining the Critical Value

After stating the hypothesis to be tested, the next step is to define the decision criterion/decision rule. This means defining the level of significance and the critical value that goes with it. The statistical tables are used to determine the critical value by using the level of significance and degree of freedom or sample size, depending on the test being conducted.

1) For {eq}t_{\alpha,v} {/eq}, {eq}\alpha {/eq} is the level of significance and v is the degree of freedom. The column of the t-table has the level of significance. The row side of the t-table is where you will find the degree of freedom. The intersection of your column (level of significance) and row (degree of freedom) will give you the corresponding t tabular value.

(a)t0.05,20 = 1.725

(b)t0.10,10 = 1.372

(c)t0.025,13 = 2.160

(d)t0.025,200 = 1.96

(e)t0.05,95 = 1.661

2) Finding the corresponding chi-square tabular value is similar to finding the t value. The columns have the alpha or the level of significance and the rows have the degree of freedom. The intersection of the column (level of significance) with the row (degree of freedom) will give you the chi-square tabular value.

(a)?20.10,5 = 9.236

(b)?20.01,100 = 135.8

(c)?20.95,18 = 9.39

(d)?20.99,60 = 37.48

3) There is one f table for every level of significance. This means that you have to make sure you are looking at the right table before proceeding to the next step. Once you found the table for the level of significance you are after, you can find the f-value by using the degree of freedom of the numerator and the degree of freedom of the denominator. The numerator degree of freedom is in the column side. On the other hand, the denominator degree of freedom can be found in the row side. The intersection of the column and the row is the f tabular value.

(a)F0.05,3,7 = 4.35

(b)F0.05,7,3 = 8.89

(c)F0.025,5,20 = 3.29

(d)F0.01,12,60 = 2.50