Manuals/calci/ZTEST

ZTEST(ar,x,sigma)

• $ar$ is the array of values.
• $x$ is the value to test.
• $sigma$ is the standard deviation of the population.

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 $ZTEST(ar,x,sigma)$,$ar$ is the array of values against which the hypothesized sample mean is to be tested.
• $x$ is the hypothesized sample mean, and $sigma$ 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 : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ZTEST(ar,\mu_0,sigma)=1-NORMSDIST((\bar{x}-μ0)/\frac{sigma}{\sqrt{n}})} .
• ZTEST is calculated when sigma is omitted and x=μ0:

Failed to parse (syntax error): {\displaystyle ZTEST(ar,μ0)=1-NORMSDIST((\bar{x}-μ0)/\frac{s}{\sqrt{n}})} where ${\bar {x}}$ is sample mean , $s$ is the sample deviation and $n$ 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: $2*MIN(ZTEST(ar,\mu _{0},sigma),1-ZTEST(ar,\mu _{0},sigma))$.
• This function will give the result as error when

    1. Any one of the argument is non-numeric.
    2. ar or x is empty.
    3. ar contains only one value.

Examples

1. Example 1

Spreadsheet

	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) = 0.9323691845
4. =2*MIN(ZTEST(A2:F2,10),1-ZTEST(A2:F2,10)) = 0.135261630850

See Also

• NORMDIST
• NORMINV
• NORMSDIST
• NORMSINV
• STANDARDIZE

References

• Z-test