Difference between revisions of "Manuals/calci/ZTEST"

Latest revision as of 03:34, 7 September 2020

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

$Array$ is the set of values.
$Mean$ is the mean value.
$StandardDeviationForPopulation$ is the standard deviation of the population.
$IsTwoTailed$ 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 $ZTEST(Array,Mean,StandardDeviationForPopulation,IsTwoTailed,Accuracy)$ , $Array$ is the array of values against which the hypothesized sample mean is to be tested.
$Mean$ is the hypothesized sample mean, and $StandardDeviationForPopulation$ 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 : $ZTEST(ar,\mu _{0},sigma)=1-NORMDIST({\bar {x}}-\mu _{0})/{\frac {sigma}{\sqrt {n}}}$
ZTEST is calculated when sigma is omitted and x=μ0:

$ZTEST(ar,\mu _{0})=1-NORMDIST({\bar {x}}-\mu _{0})/{\frac {s}{\sqrt {n}}}$ 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. Array or Mean value is empty.
    3. Array contains only one value.

Examples

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

=ZTEST(A1:G1,4) = 0.00042944272036
=2*MIN(ZTEST(A1:G1,4),1-ZTEST(A1:G1,4)) = 0.000858885440
=ZTEST(A2:F2,10) = 0.9708451547030459
=2*MIN(ZTEST(A2:F2,10),1-ZTEST(A2:F2,10)) = 0.058309690593908226

References

Z-test

List of Main Z Functions

Z3 home

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''ZTEST(ar,x,sigma)'''</div><br/>
+<div style="font-size:30px">'''ZTEST (Array,Mean,StandardDeviationForPopulation,IsTwoTailed,Accuracy)'''</div><br/>
-*<math>ar</math> is the array of values.
+*<math>Array</math> is the set of values.
-*<math>x</math>  is the value to test.
+*<math>Mean</math>  is the mean value.
-*<math>sigma</math> is the standard deviation of the population.
+*<math>StandardDeviationForPopulation</math> is the standard deviation of the population.
+*<math>IsTwoTailed</math> is the value of the tail.
+*<math>Accuracy</math> 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 <math>ZTEST(ar,x,sigma)</math>,<math> ar </math> is the array of values against which the hypothesized sample mean is to be tested.
+*In <math>ZTEST (Array,Mean,StandardDeviationForPopulation,IsTwoTailed,Accuracy)</math>,<math> Array </math> is the array of values against which the hypothesized sample mean is to be tested.
-*<math> x </math> is the  hypothesized sample mean, and <math>sigma</math> is the standard deviation of the population.
+*<math> Mean </math> is the  hypothesized sample mean, and <math>StandardDeviationForPopulation</math> 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 : <math>ZTEST(ar,\mu_0,sigma)=1-NORMSDIST((\bar{x}-μ0)/\frac{sigma}{\sqrt{n}})</math>.
+*ZTEST is calculated when sigma is not omitted and x=μ0 : <math>ZTEST(ar,\mu_0,sigma)= 1-NORMDIST(\bar{x}-\mu_0)/\frac{sigma}{\sqrt{n}}</math>
 *ZTEST is calculated when sigma is omitted and x=μ0:
-<math> ZTEST(ar,μ0)=1-NORMSDIST((\bar{x}-μ0)/\frac{s}{\sqrt{n}})</math>
+<math> ZTEST(ar,\mu_0)=1-NORMDIST(\bar{x}-\mu_0)/\frac{s}{\sqrt{n}}</math>
 where <math>\bar{x}</math> is sample mean , <math> s</math> is the sample deviation and <math>n</math> 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: <math>2*MIN(ZTEST(ar,\mu_0,sigma),1-ZTEST(ar,\mu_0,sigma))</math>.
 *This function will give the result as error when
 . Any one of the argument is non-numeric.
-. ar or x is empty.
+. Array or Mean value is empty.
-. ar contains only one value.
+. Array contains only one value.
 ==Examples==
@@ Line 37: / Line 40: @@
 #=ZTEST(A1:G1,4) = 0.00042944272036
 #=2*MIN(ZTEST(A1:G1,4),1-ZTEST(A1:G1,4)) = 0.000858885440
-#=ZTEST(A2:F2,10) = 0.9323691845
+#=ZTEST(A2:F2,10) = 0.9708451547030459
-#=2*MIN(ZTEST(A2:F2,10),1-ZTEST(A2:F2,10)) = 0.135261630850
+#=2*MIN(ZTEST(A2:F2,10),1-ZTEST(A2:F2,10)) = 0.058309690593908226
 ==Related Videos==
@@ Line 53: / Line 56: @@
 ==References==
 *[http://en.wikipedia.org/wiki/Z-test Z-test]
+*[[Z_API_Functions | List of Main Z Functions]]
+*[[ Z3 |   Z3 home ]]

Difference between revisions of "Manuals/calci/ZTEST"

Latest revision as of 03:34, 7 September 2020

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