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INFERENCE.xlsx

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INDEX

Templates for:	INFERENCE TEMPLATES
Prepared By :	Dr. Gladys E. Simpson
Last Revision:	Nov 2018
INDEX OF TEMPLATES.
Topic / Problem	SINGLE POPULATION	TWO POPULATIONS
	Z Conf. Interval -MEAN-Pop Std Deviation σ KNOWN	Z Conf. Interval -TWO MEANS-Pop Std Dev σ KNOWN
CONFIDENCE INTERVALS (CI)	T Conf. Interval -MEAN-Pop Std Dev σ UNKNOWN	T Conf. Interval -TWO MEANS-Pop Std Dev σ UNKNOWN
margin of error	Z Conf. Interval-ONE PROPORTION	Z Conf. Interval -TWO PROPORTIONS
HYPOTHESIS TESTING	Z TEST-ONE MEAN- Pop Std Dev σ KNOWN	Z TEST-TWO MEANS-σ KNOWN
P-Values, test statistic	T TEST-ONE MEAN- Pop Std Dev σ UNKNOWN	T TEST-TWO MEANS-σ UNKNOWN
	Z TEST-ONE PROPORTION	Z TEST - TWO PROPORTIONS
SAMPLE SIZE N	SAMPLE SIZE For PROPORTIONS
	SAMPLE SIZE FOR MEANS

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SAMPLE SIZE For MEANS

FINDING THE SAMPLE SIZE ( n ) for Estimation of MEANS						Back to index Page
					Fill in ORANGE spaces
		What is the confidence level ?
		hence, alpha =	100%
		critical z* =	- 0
		What is the desired error of estimation ?
		What is the Standard deviation ?
				n	ERROR:#DIV/0!
			Sample size required :		ERROR:#DIV/0!

SAMPLE SIZE For PROPORTIONS

FINDING THE SAMPLE SIZE ( n ) for PROPORTIONS						Back to index Page
					Fill in ORANGE spaces
		What is the confidence level ?
		hence, alpha =	100%
		critical z* =	- 0
		What is the desired error of estimation ?
		Approixmation of p (use 0.5 if unknown)
				n	ERROR:#DIV/0!
			Sample size required :		ERROR:#DIV/0!

CI -MEAN-σ KNOWN - using Z

FINDING A CONFIDENCE INTERVAL For a POPULATION MEAN							Back to index Page
USING EXCEL TO FIND A CONFIDENCE INTERVAL FOR THE MEAN OF A POPULATION							Z Confidence interval
					Fill in ORANGE spaces		σ KNOWN
What is the confidence level ?
hence, alpha =	100%
critical Z*	0.000
What is the sample mean ? (Point Estimate)					Finite Population ?		No
What is the sample size (n) ?							1500
What is the POPULATION Standard deviation (σ ) ?							1.000
Standard Error	ERROR:#DIV/0!
Margin of Error	ERROR:#DIV/0!
0% Confidence Interval		0	+ / -	ERROR:#DIV/0!
	From	ERROR:#DIV/0!	to	ERROR:#DIV/0!
		lower limit		upper limit

CI -MEAN-σ UNKNOWN - using t

FINDING A CONFIDENCE INTERVAL For a Population MEAN						Back to index Page
USING EXCEL TO FIND A CONFIDENCE INTERVAL FOR THE MEAN OF A POPULATION						T Confidence Interval
				Fill in ORANGE spaces		σ UNKNOWN
What is the confidence level ?		99%
hence, alpha =	1%
Degrees of Freedom	4
Critical t* for 4 df	4.604
What is the sample mean ? (Point Estimate)
What is the sample size (n) ?		5
What is the SAMPLE Standard deviation ?
Standard Error :	- 0
Margin of Error	- 0
99% Confidence Interval		0.000	±	- 0
	From	0.000	to	- 0
		lower limit		upper limit

CI-ONE PROPORTION

FINDING A CONFIDENCE INTERVAL For a PROPORTION								Back to index Page
						Fill in ORANGE spaces
What is the confidence level ?
hence, alpha =	100%
critical Z*	- 0
X - Numbero of successes				( if not given, use the proportion given to compute it: x = p * n )
What is the sample size (n) ?
Sample Proportion p (Point Estimate)			ERROR:#DIV/0!	= X / n ( enter it directly if necessary )
Std Error			ERROR:#DIV/0!	sqrt( p * ( 1 - p ) / n )
Margin of Error			ERROR:#DIV/0!	( critical z * std Error )
0% Confidence Interval	ERROR:#DIV/0!	±	ERROR:#DIV/0!	or	From	ERROR:#DIV/0!	to	ERROR:#DIV/0!	in % form
	ERROR:#DIV/0!	±	ERROR:#DIV/0!	or	From	ERROR:#DIV/0!	to	ERROR:#DIV/0!	in decimal form
						lower limit		upper limit

CI -TWO MEANS-σ KNOWN

FINDING A CONFIDENCE INTERVAL For COMPARING TWO MEANS					Back to index Page
Fill in ORANGE spaces					Z Confidence interval
What is the confidence level ?					σ KNOWN
hence, alpha =	100%
critical Z*	0.000
		Sample 1		Sample 2
What is the sample mean ?
What is the sample size (n) ?
What is the Population Std deviation (σ )?
Mean Difference (x1 - x2 )	0.000
Sampling Distrib Std dev (Std Error)	ERROR:#DIV/0!
Margin of Error	ERROR:#DIV/0!
0% Confidence Interval		0.000	±	ERROR:#DIV/0!
	From	ERROR:#DIV/0!	to	ERROR:#DIV/0!
		lower limit		upper limit

CI -TWO MEANS-σ UNKNOWN

FINDING A CONFIDENCE INTERVAL For COMPARING TWO MEANS					Back to index Page
Fill in ORANGE spaces					T Confidence Interval
What is the confidence level ?					σ UNKNOWN
hence, alpha =	100%
critical t*	ERROR:#NUM!
		Sample 1		Sample 2
What is the sample mean ?
What is the sample size (n) ?
What is the Sample Standard deviation (s) ?
Degrees of Freedom		-1		-1
Mean Difference (x1 - x2 )	0.000
Standard Error :	ERROR:#DIV/0!	Assuming Unknown and Equal Pop variances
Margin of Error	ERROR:#NUM!
0% Confidence Interval		0.000	±	ERROR:#NUM!
	From	ERROR:#NUM!	to	ERROR:#NUM!
		lower limit		upper limit

CI-TWO PROPORTIONS

CONFIDENCE INTERVAL For COMPARING TWO PROPORTIONS							Back to index Page
					Fill in ORANGE spaces
What is the confidence level ?
hence, alpha =	100%
critical z*	- 0
			Sample 1		Sample 2
X - Numbero of successes
What is the sample size (n) ?
							Difference (D)
What is the sample Proportion p			ERROR:#DIV/0!		ERROR:#DIV/0!		ERROR:#DIV/0!	ERROR:#DIV/0!
Std Error			ERROR:#DIV/0!		ERROR:#DIV/0!		ERROR:#DIV/0!
Margin of Error			ERROR:#DIV/0!	( critical z * std Error )			P-Value for D=0	ERROR:#DIV/0!
0% Confidence Interval	ERROR:#DIV/0!	±	ERROR:#DIV/0!	--> From	ERROR:#DIV/0!	to	ERROR:#DIV/0!	in % form
	ERROR:#DIV/0!	±	ERROR:#DIV/0!	--> From	ERROR:#DIV/0!	to	ERROR:#DIV/0!	in decimal form

Z TEST-ONE MEAN-σ KNOWN

SIGNIFICANCE TEST - Hypothesis test For a SINGLE Population Mean When σ KNOWN					Back to index Page
Fill in ORANGE spaces				ONE SAMPLE Z-TEST
							σ is the POPULATION STANDARD DEVIATION
Ho: Pop mean( µ ) =			Significance level				When σ is KNOWN we use the Z tables, the Normal Distribution
							TABLE A on book, or NORMDIST Excel Function
Sample mean (x)			Finite Population ?	No
Sample size ( n )
Population std dev ( σ ) =				1.000
smpl distr std dev	ERROR:#DIV/0!
test statistic z	ERROR:#DIV/0!
	ONE SIDED ALTERNATIVE				TWO SIDED
Hypotheses	Ho : µ >=	0	Ho : µ <=	0	Ho : µ =	0
	Ha : µ <	0	Ha : µ >	0	Ha : µ ≠	0
P Values	P-value	ERROR:#DIV/0!	P-value	ERROR:#DIV/0!	P-value	ERROR:#DIV/0!

T TEST-ONE MEAN-σ UNKNOWN

HYPOTHESIS TEST About A POPULATION MEAN When σ UNKNOWN					Back to index Page
Fill in ORANGE spaces				ONE SAMPLE T-TEST
						When σ ( the POPULATION STANDARD DEVIATION) is NOT KNOWN
Ho: Pop mean( µ ) =			Significance level			We use the Sample Standard deviation to estimate it
						and we work with a T DISTRIBUTION for the test statistic t
Sample mean (x)						Using TABLE D on the BOOK or TDIST Function in Excel
Sample size ( n )
Sample std dev ( s ) =
degrees of freedom
Standard Error	ERROR:#DIV/0!
test statistic t	ERROR:#DIV/0!
	1 SIDED ALTERNATIVE				TWO SIDED
Hypotheses	Ho : µ >=	0	Ho : µ <=	0	Ho : µ =	0
	Ha : µ <	0	Ha : µ >	0	Ha : µ ≠	0
P Values	P-value	ERROR:#DIV/0!	P-value	ERROR:#DIV/0!	P-value	ERROR:#DIV/0!

Z TEST-PROPORTION

HYPOTHESIS TEST About A POPULATION PROPORTION					Back to index Page						Prepared by Gladys Simpson gladys.simpson@fiu.edu
Fill in ORANGE spaces			Z-TEST FOR A PROPORTION						If the sample size is too small, inference for proportions must be based on binomial distribution
									when the sample is large, both the count X and the sample proportion are
Ho: Pop proportion p0 =			Significance level (alpha)						approximately normal and we work with the normal distribution.
									Here we work with the normal distribution.
X number of successes
									IT is recommended to use large-sample z significance tst as long as the
Sample size ( n )									expected number of successes ( np) and expected failures (nq) are both greater than 5
Sample Proportion p	ERROR:#DIV/0!	(x/n) - Number of successes / sample size							CAN'T USE THIS TEST when sample is too small
Hence, pop std dev =	- 0
Standard Error	ERROR:#DIV/0!
test statistic z	ERROR:#DIV/0!
	1 SIDED ALTERNATIVE				TWO SIDED
Hypotheses	Ho : p >=	0%	Ho : p < =	0%	Ho : p =	0%
	Ha : p <	0%	Ha : p >	0%	Ha : p ≠	0%
P Values	P-value	ERROR:#DIV/0!	P-value	ERROR:#DIV/0!	P-value	ERROR:#DIV/0!

Z TEST-TWO MEANS-σ KNOWN

COMPARING TWO MEANS - Hypothesis test for Differences in sample means - σ KNOWN						Back to index Page
			Fill in ORANGE spaces		TWO SAMPLE Z-TEST				When σ ( the POPULATION STANDARD DEVIATION) is KNOWN
Significance level
	Sample 1		Sample 2						We use the Sample Standard deviation to estimate it
Sample mean (x)									we work with a Z DISTRIBUTION for the test statistic (Z)
Sample size ( n )
Population std dev ( σ ) =
Mean difference (x1-x2)	0.00
Standard Error	ERROR:#DIV/0!
test statistic Z	ERROR:#DIV/0!
	1 SIDED ALTERNATIVE				TWO SIDED
Hypotheses	Ho : µ1 = µ2		Ho : µ1 = µ2		Ho : µ1 = µ2
	Ha : µ1 < µ2		Ha : µ1 > µ2		Ha : µ1 ≠ µ2
P Values	P-value	ERROR:#DIV/0!	P-value	ERROR:#DIV/0!	P-value	ERROR:#DIV/0!

T TEST-TWO MEANS-σ UNKNOWN

COMPARING TWO MEANS - Hypothesis test for Difference in TWO POPULATION MEANS						Back to index Page
Fill in ORANGE spaces					TWO SAMPLE T-TEST				When σ ( the POPULATION STANDARD DEVIATION) is NOT KNOWN
Significance level									We use the Sample Standard deviation to estimate it
									and we work with a T DISTRIBUTION for the test statistic t
	Sample 1		Sample 2						Using TABLE D on the BOOK or TDIST Function in Excel
Sample mean (x)
Sample size ( n )
Sample std dev ( s ) =
Mean difference (x1-x2)	0.000
degrees of freedom	-1		-1
Standard Error	ERROR:#DIV/0!	Assuming Equal Variances
test statistic t	ERROR:#DIV/0!
	1 SIDED ALTERNATIVE				TWO SIDED
Hypotheses	Ho : µ1 = µ2		Ho : µ1 = µ2		Ho : µ1 = µ2
	Ha : µ1 < µ2		Ha : µ1 > µ2		Ha : µ1 ≠ µ2
P Values	P-value	ERROR:#DIV/0!	P-value	ERROR:#DIV/0!	P-value	ERROR:#DIV/0!

Z TEST - TWO PROPORTIONS

FINDING THE P-VALUE and HYPOTHESIS TEST for PROPORTIONS						Back to index Page					Prepared by Gladys Simpson gladys.simpson@fiu.edu
Fill in ORANGE spaces				Z-TEST FOR COMPARING TWO PROPORTIONS
Significance level
	Sample 1		Sample 2		Overall
X number of successes					0
Sample size ( n )					0
Sample Proportion p	ERROR:#DIV/0!		ERROR:#DIV/0!		ERROR:#DIV/0!
Standard Error	ERROR:#DIV/0!		ERROR:#DIV/0!		ERROR:#DIV/0!
test statistic Z	ERROR:#DIV/0!
Hypotheses	Ho : p1 = p2		Ho : p1 = p2		Ho : p1 = p2
	Ha : p1 < p2		Ha : p1 > p2		Ha : p1 ≠ p2
P Values	P-value	ERROR:#DIV/0!	P-value	ERROR:#DIV/0!	P-value	ERROR:#DIV/0!