# Manuals/calci/ZTEST

ZTEST (Array,Mean,StandardDeviationForPopulation,IsTwoTailed,Accuracy)

• is the set of values.
• is the mean value.
• is the standard deviation of the population.
• is the value of the tail.
• gives accurate value of the solution.
• ZTEST() returns the one-tailed probability-value of a z-test.

## Description

• This function gives the one-tailed probability of z-test.
• Z-test is used to determine whether two population means are different when the variances are known and the sample size is large.
• In , is the array of values against which the hypothesized sample mean is to be tested.
• is the hypothesized sample mean, and is the standard deviation of the population.
• When we are not giving the sigma value, it will use the standard deviation of sample.
• This function returns the probability that the supplied hypothesized sample mean is greater than the mean of the supplied data values.
• The test statistic should follow a normal distribution.
• ZTEST is calculated when sigma is not omitted and x=μ0 :
• ZTEST is calculated when sigma is omitted and x=μ0:

where is sample mean , is the sample deviation and is the size of the sample.

• Suppose we want to calculate the z-test for two tailed probability then this can be done by using the Z_test function: .
• This function will give the result as error when
    1. Any one of the argument is non-numeric.
2. Array or Mean value is empty.
3. Array contains only one value.


## Examples

1. Example 1
A B C D E F G
1 10 15 7 2 19 20 12
2 3 4 8 1 10 15 5
1. =ZTEST(A1:G1,4) = 0.00042944272036
2. =2*MIN(ZTEST(A1:G1,4),1-ZTEST(A1:G1,4)) = 0.000858885440
3. =ZTEST(A2:F2,10) = 0.9708451547030459
4. =2*MIN(ZTEST(A2:F2,10),1-ZTEST(A2:F2,10)) = 0.058309690593908226

Z-TEST