Manuals/calci/ZTESTEQUALMEANS

ZTESTTWOSAMPLEFORMEANS(ar1,ar2,v1,v2,md,alpha,lv)

• $ar1$ and $ar2$ are array of values.
• $v1$ and $v2$ are value of variances.
• $md$ is the Hypothesized Mean Difference.
• $alpha$ is the significance level.
• $lv$ is the logical value.

Description

• This function gives the z-test two sample for means.
• We can use this test when

1.The samples can be different sizes.
2.The two samples are independent.
3.Both populations are normally distributed or both sample sizes are large enough that the means are normally distributed.

• In $ZTESTTWOSAMPLEFORMEANS(ar_{1},ar_{2},v_{1},v_{2},md,alpha,lv)$,$ar_{1}$ and $ar_{2}$ are the set of values,$v_{1}$ is the variance of $ar_{1}$,$v_{2}$ is the variance of $ar_{2}$.
• $md$ is the Hypothesized Mean Difference. If testing is for equal means,then $md=0$.
• $alpha$ is the significance level which ranges from 0 to 1.
• $lv$ is the logical value like TRUE or FALSE.TRUE is indicating the result will display in new worksheet.
• Suppose we are omitted the $lv$ value it will consider the value as FALSE.
• ZTEST two sample for means is calculated by:$z={\frac {{\bar {x_{1}}}-{\bar {x_{2}}}-\Delta }{\sqrt {{\frac {\sigma _{1}^{2}}{n_{1}}}+{\frac {\sigma _{2}^{2}}{n_{2}}}}}}$

where ${\bar {x_{1}}}$ and Failed to parse (unknown function "\math"): {\displaystyle \bar{x_2}<\math> are average of two samples, <math>\Delta} is the Hypothesized Mean Difference between two means of the population. $\sigma _{1}$ and $\sigma _{2}$ are the standard deviation of two population. <math> n_1 <\math> and <math> n_2 <\math> are the sizes of the samples.

• This function will give the result as error when

 1. any one of the argument is nonnumeric.
 2. alpha>1

and ar2 are array of values, and v2 ,  ,  and  

ZTESTTWOSAMPLEFORMEANS(Array1, Array2, Variance1, Variance2, Alpha, NewTableFlag)

where,

Array1 - Input range should be one block.

Array2 - Input range should be one block.

Variance1 - Input range should be one block.

Variance2 - Input range should be one block.

HypothesizeDiff - represents the Hypothesized Mean Difference.A value 0 indicates that sample means are hypothesized to be equal.

Alpha - represents the significance level and value in range 0 to 1.

' 'NewTableFlag - is the TRUE or FALSE.If set as TRUE,the result in new sheet. If NewTableFlag is omitted, it assumed to be FALSE.

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T-Test: Two Sample for unequal variances determines whether two sample means are distinct.

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Lets see an example in (Column4Row5)

?UNIQbb01b3076906c32b-nowiki-00000004-QINU?

ZTESTTWOSAMPLESFORMEANS returns the result in new sheet(5Space).

?UNIQbb01b3076906c32b-nowiki-00000005-QINU?

ZTESTTWOSAMPLESFORMEANS returns the #ERROR(Alpha = -0.055).

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Z-TEST : TWO SAMPLE  FOR MEANS

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Syntax

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Remarks

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Examples

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Description

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If the Alpha < 0 or Alpha >1, ZTESTTWOSAMPLEFORMEANS returns the #ERROR.

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	Column1	Column2	Column3	File:Copy-cube.gif  Column4
Row1	10	3	1	8
Row2	7	8	2	9
Row3	12	8	3	10
Row4	17	18	4	11
Row5	46	34		5Space
Row6	6	7	#ERROR

File:Calci1.gif

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z-Test: Two Sample for Means

	Variable1	Variable2
Mean	11.5	9.25
Known Variance	1,2,3,4	8,9,10,11
Observations	4	4
Hypothesized Mean Difference	0
z Value	NaN
P(T<=t) One-tail	0
z Critical One-tail	1.6448536269514715
P(T<=t) Two-tail	0
z Critical Two-tail	1.9599639845400536

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