Margin of Error

(CAP P)

Khan Academy's videos on Standard Error https://www.khanacademy.org/math/ap-statistics/sampling-distribution-ap/sampling-distribution-mean/v/standard-error-of-the-mean

The question assumes a Sample is being used to estimate a population mean μμ

• Sample Size =30

• Sample Mean = ¯xx¯ = 40

• Sample Standard Deviation = 2

Find the Margin of Error at a 90% CI

The Website " Statistics How to" - has a great example http://www.statisticshowto.com/how-to-calculate-margin-of-error Lets use this web pages video as a sample for how to answer our "Find the Margin of Error" for our question.

Here is a slightly different written question of the "Statistics How to" page.

A margin-of-error tells you how many percentage points your results will differ from the real population value. For example, a 95% confidence interval with a 4 percent margin of error means that your statistic will be within 4 percentage points of the real population value 95% of the time.

The Margin of Error can be calculated in two ways:

1. Margin-of-error = Critical value x Standard deviation <-- IF you have all the data from the population (very rare) so we use the next formula.

2. Margin of error = Critical value x Standard error of the statistic

This means that MOST OF THE TIME - when you are dealing with SAMPLES you need to use the formula

Margin of error = Critical value x Standard error of the statistic

We need to get the CV-Critical Value AND the SE-Standard Error

Margin of Error video https://www.youtube.com/watch?time_continue=125&v=MV_BwPHWGh8

The "Statistics How to" has a page that explains how to calculate the Critical Value

Critical Value is obtained by knowing the CI-Confidence Interval - we can use a Lookup Table

Video - how to find the Critical value for a CI - https://www.youtube.com/watch?v=RAnFyF_6zHk

• CI of 50% = 0.674 z value = Critical Value

• CI of 80% = 1.282 z value = Critical Value

• CI of 90% = 1.645 z value = Critical Value

• CI of 95% = 1.960 z value = Critical Value

• CI of 98% = 2.326 z value = Critical Value

• CI of 99% = 2.576 z Value = Critical Value

We also need to fine the SE = Standard Error = Standard Deviation / Sqrt of the sample size.

Video - how to calculate the Standard Error - https://www.youtube.com/watch?v=aBXJnvQ6KFk

Formula for SE Standard Error = Standard Deviation / SQRT of Sample Size = 2 / sqrt(30)

More about Standard Error https://www.youtube.com/watch?v=BwYj69LAQOI

we can now plug these number into our Margin of Error Formula

2. Margin of error = Critical value x Standard error of the statistic

= 1.645 * 2 / sqrt(30)

Margin of Error for a PROPORTION

Margin of Error for a Proportion

The formula is a little different for proportions: