Difference between revisions of "Manuals/calci/ZTEST"

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<div style="font-size:30px">'''ZTEST(ar,x,sigma)'''</div><br/>
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<div style="font-size:30px">'''ZTEST (Array,Mean,StandardDeviationForPopulation,IsTwoTailed,Accuracy)'''</div><br/>
*<math>ar</math> is the array of values.
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*<math>Array</math> is the set of values.
*<math>x</math>  is the value to test.
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*<math>Mean</math>  is the mean value.
*<math>sigma</math> is the standard deviation of the population.
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*<math>StandardDeviationForPopulation</math> is the standard deviation of the population.
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*<math>IsTwoTailed</math> is the value of the tail.
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*<math>Accuracy</math> gives accurate value of the solution.
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**ZTEST() returns the one-tailed probability-value of a z-test.
  
 
==Description==
 
==Description==
 
*This function gives the one-tailed probability of z-test.  
 
*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.
 
*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.
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*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.  
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*<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.  
 
*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.
 
*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.  
 
*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>.
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*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:
 
*ZTEST is calculated when sigma is omitted and x=μ0:
<math> ZTEST(ar,μ0)=1-NORMSDIST((\bar{x}-μ0)/\frac{s}{\sqrt{n}})</math>
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<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.  
 
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>.  
 
*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  
 
*This function will give the result as error when  
 
     1. Any one of the argument is non-numeric.
 
     1. Any one of the argument is non-numeric.
     2. ar or x is empty.
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     2. Array or Mean value is empty.
     3. ar contains only one value.
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     3. Array contains only one value.
  
 
==Examples==
 
==Examples==
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#=ZTEST(A1:G1,4) = 0.00042944272036
 
#=ZTEST(A1:G1,4) = 0.00042944272036
 
#=2*MIN(ZTEST(A1:G1,4),1-ZTEST(A1:G1,4)) = 0.000858885440
 
#=2*MIN(ZTEST(A1:G1,4),1-ZTEST(A1:G1,4)) = 0.000858885440
#=ZTEST(A2:F2,10) = 0.9323691845
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#=ZTEST(A2:F2,10) = 0.9708451547030459
#=2*MIN(ZTEST(A2:F2,10),1-ZTEST(A2:F2,10)) = 0.135261630850
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#=2*MIN(ZTEST(A2:F2,10),1-ZTEST(A2:F2,10)) = 0.058309690593908226
  
 
==Related Videos==
 
==Related Videos==
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==References==
 
==References==
 
*[http://en.wikipedia.org/wiki/Z-test Z-test]
 
*[http://en.wikipedia.org/wiki/Z-test Z-test]
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 04:34, 7 September 2020

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
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) = 0.9708451547030459
  4. =2*MIN(ZTEST(A2:F2,10),1-ZTEST(A2:F2,10)) = 0.058309690593908226

Related Videos

Z-TEST

See Also

References