Difference between revisions of "Manuals/calci/ZTEST"
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− | <div style="font-size:30px">'''ZTEST( | + | <div style="font-size:30px">'''ZTEST (Array,Mean,StandardDeviationForPopulation,IsTwoTailed,Accuracy)'''</div><br/> |
− | *<math> | + | *<math>Array</math> is the set of values. |
− | *<math> | + | *<math>Mean</math> is the mean value. |
− | *<math> | + | *<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== | ==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( | + | *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> | + | *<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- | + | *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, | + | <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. | + | 2. Array or Mean value is empty. |
− | 3. | + | 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. | + | #=ZTEST(A2:F2,10) = 0.9708451547030459 |
− | #=2*MIN(ZTEST(A2:F2,10),1-ZTEST(A2:F2,10)) = 0. | + | #=2*MIN(ZTEST(A2:F2,10),1-ZTEST(A2:F2,10)) = 0.058309690593908226 |
==Related Videos== | ==Related Videos== | ||
Line 53: | Line 56: | ||
==References== | ==References== | ||
*[http://en.wikipedia.org/wiki/Z-test Z-test] | *[http://en.wikipedia.org/wiki/Z-test Z-test] | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | *[[Z_API_Functions | List of Main Z Functions]] | ||
+ | |||
+ | *[[ 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
- 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 |
- =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
Related Videos
See Also
References