# How to Find Z Critical Values in R

Whenever you conduct a hypothesis test, you will get a test statistic as a result. To determine if the results of the hypothesis test are statistically significant, you can compare the test statistic to a Z critical value. If the absolute value of the test statistic is greater than the Z critical value, then the results of the test are statistically significant.

To find the Z critical value in R, you can use the qnorm() function, which uses the following syntax:

qnorm(p, mean = 0, sd = 1, lower.tail = TRUE)

where:

• p: The significance level to use
• mean: The mean of the normal distribution
• sd: The standard deviation of the normal distribution
• lower.tail: If TRUE, the probability to the left of 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 Z critical value for a left-tailed test, right-tailed test, and a two-tailed test.

### Left-tailed test

Suppose we want to find the Z critical value for a left-tailed test with a significance level of .05:

```#find Z critical value
qnorm(p=.05, lower.tail=TRUE)

 -1.644854
```

The Z critical value is -1.644854. Thus, if the test statistic is less than this value, the results of the test are statistically significant.

### Right-tailed test

Suppose we want to find the Z critical value for a right-tailed test with a significance level of .05:

```#find Z critical value
qnorm(p=.05, lower.tail=FALSE)

 1.644854
```

The Z critical value is 1.644854. Thus, if the test statistic is greater than this value, the results of the test are statistically significant.

### Two-tailed test

Suppose we want to find the Z critical value for a two-tailed test with a significance level of .05:

```#find Z critical value
qnorm(p=.05/2, lower.tail=FALSE)

 1.959964
```

Whenever you perform a two-tailed test, there will be two critical values. In this case, the Z critical values are 1.959964 and -1.959964. Thus, if the test statistic is less than -1.959964 or greater than 1.959964, the results of the test are statistically significant.

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