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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 [email protected]
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 ( n*p) and expected failures (n*q) 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 [email protected]
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!