See attachment.
© 2023
One-Tailed and Two-Tailed Test
One-Tailed Test
Alternate Indicates Greater Than
Assume a= .05 and HO:µ :5: µO vs. Ha:µ> µO. This is called a one-tailed test because the null hypothesis
will be rejected if the value of the test statistic is too large. All of the values of a will be in the right tail of
the normal curve. Note the inequality in the alternative points in the direction of the rejection region.
When the value of the test statistic is greater than z, the null hypothesis will be rejected; otherwise, it will
not be rejected-often stated as failure to reject the null hypothesis. The shaded area represents the
area where the null hypothesis would be rejected.
The table below lists some common values for z* when the alternative is one tailed, or contains the
greater than (>) symbol.
Confidence (C) A
90% a= .10
95% a=.05
99% a= .01
Critical Value (z*)
+1.28
+1.645
+3.10
Page 2 of4 Biostatistical Methods
©2023 South University
One-Tailed and Two-Tailed Test
Alternate Indicates Less Than
Assume a= .05 and HO:µ� µO vs. Ha:µ< µO. This is called a one-tailed test because the null hypothesis
will be rejected if the value of the test statistic is too small. All of the values of a will be in the left tail of
the normal curve. Note the inequality in the alternative points in the direction of the rejection region.
-z”
When the value of the test statistic is less than -z, the null hypothesis will be rejected; otherwise, it will
not be rejected-often stated as failure to reject the null hypothesis. The shaded area represents the
area where the null hypothesis would be rejected.
The table below lists some common values for z* when the alternative is one tailed, or contains the less
than(<) symbol.
Confidence (C) a
90% a= .10
95% a=.05
99% a= .01
Critical Value (z*)
-1.28
-1.645
-3.10
Page 3 of4 Biostatistical Methods
©2023 South University
One-Tailed and Two-Tailed Test
Two-Tailed Test
Assume C = 95%, which means a= .05 and HO:µ= µO vs. Ha:µ ;t:. µO. This is called a two-tailed test since
the null hypothesis will be rejected if the value of the test statistic is too small or too large. Half the value
of a will be in each tail of the normal curve-a/2 = .025.
When the value of the test statistic is less than -z or greater than +z, the null hypothesis will be rejected;
otherwise, it will not be rejected-often stated as failure to reject the null hypothesis. The shaded area
represents the area where the null hypothesis would be rejected.
The table below lists some common values for z* when the alternative is two tailed, or contains the not
equal to (;t:.) symbol.
Confidence (C) a
90% a= .10; a/2 = .05
95% a = .05; a/2 = .025
99% a= .01; a/2 = .005
Critical Value (z*)
± 1.645
± 1.96
± 2.576
Page4of4 Biostatistical Methods
©2023 South University
