PHE5020 - Week 1 Project

© 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