Margin of Error

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Presentation Description

How to calculate margin of error and confidence interval estimates.

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Presentation Transcript

Margin of Error : 

Margin of Error & Confidence Intervals headlessprofessor

When this applies : 

When this applies A sample is being used to estimate a population mean

What it tells you : 

What it tells you How far off your estimate is likely to be

What you need : 

What you need Sample size = N

What you need : 

What you need Sample size = N Sample mean

What you need : 

What you need Sample mean & N Standard deviation

What you need : 

What you need Sample mean & N Standard deviation Z score for level of confidence

What you need : 

What you need Sample mean & N Standard deviation Z score for level of confidence (z = 1.96)

How to Calculate : 

How to Calculate Standard Deviation Divided by Square Root Of Sample Size

How to Calculate : 

How to Calculate Standard Deviation Divided by Square Root Of Sample Size (standard error)

How to Calculate : 

How to Calculate Margin of Error = Standard Error times Z score

Example : 

Example N = 49 Mean = 78 Std Dev = 5 Z score = 1.96

How to Calculate : 

How to Calculate Square root of sample size = Square root of 49 = 7

How to Calculate : 

How to Calculate Standard deviation divided by square root of sample size 5 / 7

How to Calculate : 

How to Calculate Standard deviation divided by square root of sample size 5 / 7 = 0.714

How to Calculate : 

How to Calculate Standard deviation divided by square root of sample size 5 / 7 = 0.714 Standard Error

How to Calculate : 

How to Calculate Standard deviation divided by square root of sample size 5 / 7 = 0.714 Standard Error

How to Calculate : 

How to Calculate Margin of Error = Std Error X Z 0.714 X 1.96

How to Calculate : 

How to Calculate Margin of Error = Std Error X Z 0.714 X 1.96 = 1.40

What this means : 

What this means Margin of Error: 95% of the time, the population mean will be within 1.40 of the mean

Confidence Interval : 

Confidence Interval The range of scores from mean – ME to mean + ME

Example of Confidence Interval : 

Example of Confidence Interval The range of scores from 78 – 1.40 to 78 + 1.40

Example of Confidence Interval : 

Example of Confidence Interval The range of scores from – 1.40 to 78 + 1.40 76.6 to 79.4

To get narrower : 

To get narrower Have a lower standard deviation

To get narrower : 

To get narrower Have a lower standard deviation Accept a lower level of confidence (e.g., .90 instead of .95)

To get narrower : 

To get narrower Have a lower standard deviation Accept a lower level of confidence (e.g., .90 instead of .95) Use a larger sample size N

To get a better level of confidence : 

To get a better level of confidence Have a lower standard deviation

To get a better level of confidence : 

To get a better level of confidence Have a lower standard deviation Accept a broader confidence interval

To get a better level of confidence : 

To get a better level of confidence Have a lower standard deviation Accept a broader confidence interval Use a larger sample size

Use T instead of Z : 

Use T instead of Z When population SD is not known

Use T instead of Z : 

Use T instead of Z When population SD is not known Use df = N - 1

Margin of Error : 

Margin of Error & Confidence Intervals headlessprofessor