Often in statistics we’re interested in determining the p-value associated with a certain z-score that results from a hypothesis test. If this p-value is below some significance level, we can reject the null hypothesis of our hypothesis test.

To find the p-value associated with a z-score in R, we can use the pnorm() function, which uses the following syntax:

**pnorm(q, mean = 0, sd = 1, lower.tail = TRUE)**

where:

**q:**The z-score**mean:**The mean of the normal distribution. Default is 0.**sd:**The standard deviation of the normal distribution. Default is 1.**lower.tail:**If TRUE, the probability to the left of**q**in the normal distribution is returned. If FALSE, the probability to the right is returned. Default is TRUE.

The following examples illustrate how to find the p-value associated with a z-score for a left-tailed test, right-tailed test, and a two-tailed test.

**Left-tailed test**

Suppose we want to find the p-value associated with a z-score of **-0.77** in a left-tailed hypothesis test.

#find p-value pnorm(q=-0.77, lower.tail=TRUE) [1] 0.2206499

The p-value is **0.2206**. If we use a significance level of α = 0.05, we would fail to reject the null hypothesis of our hypothesis test because this p-value is not less than 0.05.

**Right-tailed test**

Suppose we want to find the p-value associated with a z-score of **1.87** in a right-tailed hypothesis test.

#find p-value pnorm(q=1.87, lower.tail=FALSE) [1] 0.03074191

The p-value is **0.0307**. If we use a significance level of α = 0.05, we would reject the null hypothesis of our hypothesis test because this p-value is less than 0.05.

**Two-tailed test**

Suppose we want to find the p-value associated with a z-score of **1.24** in a two-tailed hypothesis test.

#find p-value for two-tailed test 2*pnorm(q=1.24, lower.tail=FALSE) [1] 0.2149754

*To find this two-tailed p-value we simply multiplied the one-tailed p-value by two.*

The p-value is **0.2149**. If we use a significance level of α = 0.05, we would fail to reject the null hypothesis of our hypothesis test because this p-value is not less than 0.05.

**Related: **You can also use this online Z Score to P Value Calculator to find p-values.