# Find Critical Value of t for One Tailed t-Test

Student's t-distribution table & how to use instructions to quickly find the table or critical (rejection region) value of t at a stated level of significance (α) to check if the test of hypothesis (H0) for one (right or left) tailed t-test is accepted or rejected in statistics & probability experiments to analyze the small samples. The degrees of freedom is used to refer the t-table values at a specified level of significance such as 1%, 2%, 3%, 4%, 5%, 10%, 25%, 50% etc. It's generally represented by te. In one (right or left) tailed Student's t-test, the calculated value of t or t-statistic (t0) is compared with the table or critical value of t to check if the null hypothesis is accepted or rejected in the statistical experiments include small sample size. This students's t-table for one tailed t-test is also available in pdf format too, users may download this table in pdf format to refer it later offline.

In one tailed t-tests, the critical value of t from t-distribution table represents the rejection area of distribution either left or right of the mean. In single tailed t-test, the critical value of t at a specified level of significance (α) is calculated either left side or right side of the mean of t-distribution. Whereas, in two tailed t-test, the critical value of t at a specified level of significance (α) is calculated for both left & right side of the mean of t-distribution but the α value is divided by 2 and corresponding critical value of t is derived from the t-distribution table for both halves. For example, t0.5 of single tailed test equals to t(0.25) of two tailed test.

In other words, a single tailed t-test at 10% significance level have the rejection area either in left or right side of the mean, while for two tailed t-test at 10% significance level have 5% rejection area on the left side & remaining 5% rejection area on the right side of the mean.

One Tailed Student's t-Distribution Table
αdf 0.010.030.050.10.20.250.5
1  127.32   63.66   21.20   12.71   6.31   5.03   2.41
2  14.09   9.92   5.64   4.30   2.92   2.56   1.60
3  7.45   5.84   3.90   3.18   2.35   2.11   1.42
4  5.60   4.60   3.30   2.78   2.13   1.94   1.34
5  4.77   4.03   3.00   2.57   2.02   1.84   1.30

6  4.32   3.71   2.83   2.45   1.94   1.78   1.27
7  4.03   3.50   2.71   2.36   1.89   1.74   1.25
8  3.83   3.36   2.63   2.31   1.86   1.71   1.24
9  3.69   3.25   2.57   2.26   1.83   1.69   1.23
10  3.58   3.17   2.53   2.23   1.81   1.67   1.22

11  3.50   3.11   2.49   2.20   1.80   1.66   1.21
12  3.43   3.05   2.46   2.18   1.78   1.65   1.21
13  3.37   3.01   2.44   2.16   1.77   1.64   1.20
14  3.33   2.98   2.41   2.14   1.76   1.63   1.20
15  3.29   2.95   2.40   2.13   1.75   1.62   1.20

16  3.25   2.92   2.38   2.12   1.75   1.62   1.19
17  3.22   2.90   2.37   2.11   1.74   1.61   1.19
18  3.20   2.88   2.36   2.10   1.73   1.61   1.19
19  3.17   2.86   2.35   2.09   1.73   1.60   1.19
20  3.15   2.85   2.34   2.09   1.72   1.60   1.18

21  3.14   2.83   2.33   2.08   1.72   1.60   1.18
22  3.12   2.82   2.32   2.07   1.72   1.59   1.18
23  3.10   2.81   2.31   2.07   1.71   1.59   1.18
24  3.09   2.80   2.31   2.06   1.71   1.59   1.18
25  3.08   2.79   2.30   2.06   1.71   1.59   1.18

26  3.07   2.78   2.30   2.06   1.71   1.59   1.18
27  3.06   2.77   2.29   2.05   1.70   1.58   1.18
28  3.05   2.76   2.29   2.05   1.70   1.58   1.17
29  3.04   2.76   2.28   2.05   1.70   1.58   1.17
30  3.03   2.75   2.28   2.04   1.70   1.58   1.17

31  3.02   2.74   2.27   2.04   1.70   1.58   1.17
32  3.01   2.74   2.27   2.04   1.69   1.58   1.17
33  3.01   2.73   2.27   2.03   1.69   1.57   1.17
34  3.00   2.73   2.27   2.03   1.69   1.57   1.17
35  3.00   2.72   2.26   2.03   1.69   1.57   1.17

36  2.99   2.72   2.26   2.03   1.69   1.57   1.17
37  2.99   2.72   2.26   2.03   1.69   1.57   1.17
38  2.98   2.71   2.25   2.02   1.69   1.57   1.17
39  2.98   2.71   2.25   2.02   1.68   1.57   1.17
40  2.97   2.70   2.25   2.02   1.68   1.57   1.17

41  2.97   2.70   2.25   2.02   1.68   1.57   1.17
42  2.96   2.70   2.25   2.02   1.68   1.57   1.17
43  2.96   2.70   2.24   2.02   1.68   1.56   1.17
44  2.96   2.69   2.24   2.02   1.68   1.56   1.17
45  2.95   2.69   2.24   2.01   1.68   1.56   1.17

46  2.95   2.69   2.24   2.01   1.68   1.56   1.17
47  2.95   2.68   2.24   2.01   1.68   1.56   1.16
48  2.94   2.68   2.24   2.01   1.68   1.56   1.16
49  2.94   2.68   2.24   2.01   1.68   1.56   1.16
50  2.94   2.68   2.23   2.01   1.68   1.56   1.16

51  2.93   2.68   2.23   2.01   1.68   1.56   1.16
52  2.93   2.67   2.23   2.01   1.67   1.56   1.16
53  2.93   2.67   2.23   2.01   1.67   1.56   1.16
54  2.93   2.67   2.23   2.00   1.67   1.56   1.16
55  2.92   2.67   2.23   2.00   1.67   1.56   1.16

56  2.92   2.67   2.23   2.00   1.67   1.56   1.16
57  2.92   2.66   2.23   2.00   1.67   1.56   1.16
58  2.92   2.66   2.22   2.00   1.67   1.56   1.16
59  2.92   2.66   2.22   2.00   1.67   1.56   1.16
60  2.91   2.66   2.22   2.00   1.67   1.56   1.16

61  2.91   2.66   2.22   2.00   1.67   1.56   1.16
62  2.91   2.66   2.22   2.00   1.67   1.56   1.16
63  2.91   2.66   2.22   2.00   1.67   1.55   1.16
64  2.91   2.65   2.22   2.00   1.67   1.55   1.16
65  2.91   2.65   2.22   2.00   1.67   1.55   1.16

66  2.90   2.65   2.22   2.00   1.67   1.55   1.16
67  2.90   2.65   2.22   2.00   1.67   1.55   1.16
68  2.90   2.65   2.22   2.00   1.67   1.55   1.16
69  2.90   2.65   2.22   1.99   1.67   1.55   1.16
70  2.90   2.65   2.22   1.99   1.67   1.55   1.16

71  2.90   2.65   2.21   1.99   1.67   1.55   1.16
72  2.90   2.65   2.21   1.99   1.67   1.55   1.16
73  2.89   2.64   2.21   1.99   1.67   1.55   1.16
74  2.89   2.64   2.21   1.99   1.67   1.55   1.16
75  2.89   2.64   2.21   1.99   1.67   1.55   1.16

76  2.89   2.64   2.21   1.99   1.67   1.55   1.16
77  2.89   2.64   2.21   1.99   1.66   1.55   1.16
78  2.89   2.64   2.21   1.99   1.66   1.55   1.16
79  2.89   2.64   2.21   1.99   1.66   1.55   1.16
80  2.89   2.64   2.21   1.99   1.66   1.55   1.16

81  2.89   2.64   2.21   1.99   1.66   1.55   1.16
82  2.88   2.64   2.21   1.99   1.66   1.55   1.16
83  2.88   2.64   2.21   1.99   1.66   1.55   1.16
84  2.88   2.64   2.21   1.99   1.66   1.55   1.16
85  2.88   2.63   2.21   1.99   1.66   1.55   1.16

86  2.88   2.63   2.21   1.99   1.66   1.55   1.16
87  2.88   2.63   2.21   1.99   1.66   1.55   1.16
88  2.88   2.63   2.21   1.99   1.66   1.55   1.16
89  2.88   2.63   2.21   1.99   1.66   1.55   1.16
90  2.88   2.63   2.21   1.99   1.66   1.55   1.16

91  2.88   2.63   2.20   1.99   1.66   1.55   1.16
92  2.88   2.63   2.20   1.99   1.66   1.55   1.16
93  2.88   2.63   2.20   1.99   1.66   1.55   1.16
94  2.87   2.63   2.20   1.99   1.66   1.55   1.16
95  2.87   2.63   2.20   1.99   1.66   1.55   1.16

96  2.87   2.63   2.20   1.98   1.66   1.55   1.16
97  2.87   2.63   2.20   1.98   1.66   1.55   1.16
98  2.87   2.63   2.20   1.98   1.66   1.55   1.16
99  2.87   2.63   2.20   1.98   1.66   1.55   1.16
100  2.87   2.63   2.20   1.98   1.66   1.55   1.16

## How to Find Critical Region in Student's t-Test

Users may use this below single tailed t-table calculator or refer the rows & columns value of t-distribution table to find the critical region of t-distribution.
by Using Calculator
Supply or select the values of type of t-test (one tailed) such as degrees of freedom (df) and significance level (α) directly to the single tailed t-table calculator and hit on "LOCATE" to locate the corresponding critical value of t.

by Using t-Distribution Table
Refer the significance level α value in the row & degrees of freedom df in the column. The point where the row & column meets for the corresponding value is the critical value of t or the rejection area of one (left or right tailed) t-distribution.

## Inference

The below statements show when to accept or reject null hypothesis H0 in one (right or left) tailed t-test

For null hypothesis H0 :
If t0 < te then the null hypothesis H0 is accepted.
It states that there is no significance difference between t-statistic & expected value of t.

If t0 > te then the null hypothesis H0 is rejected.
It states that there is significance difference between t-statistic & expected value of t.