{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lect16v4_1up

# lect16v4_1up - Stat 104 Quantitative Methods for Economists...

This preview shows pages 1–15. Sign up to view the full content.

Stat 104: Quantitative Methods for Economists Class 16: Confidence Intervals- One Sample Mean 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Say we have a population of interest and we want to determine what its mean is. μ = ? Population Introduction 2 We know the procedure is to generate a random sample X 1 X 2 ,..., X n and form the estimate X n X i i n = = 1 1
It would be grossly misleading to claim that μ is precisely equal to the observed X How Wrong Are We ? To detail our uncertainty about our estimate for μ, we can construct a confidence interval or interval estimate for μ . Example: what is the average weight of graduate students’ at Harvard ? point estimates interval estimates Gender Sample Mean Std. Err. DF L. Limit U. Limit 0 168.52577 2.663393 96 163.23898 173.81256 1 126.34821 3.4025612 55 119.52933 133.1671 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The same idea works for proportions. What proportion of students are right handed ? Gender Count Total Sample Prop. Std. Err. L. Limit U. Limit 0 90 98 0.9183673 0.027658405 0.86415786 0.9725768 1 56 58 0.9655172 0.023958908 0.91855866 1.0124758 (silly?) Confidence intervals are a vital aspect to statistics since an estimate is useless without some concept of its precision-that is exactly what a confidence interval tells us; how good is our estimate . 4
Point and Interval Estimates square6 A point estimate is a single number, square6 a confidence interval provides additional information about variability Point Estimate Lower Confidence Limit Upper Confidence Limit Width of confidence interval 5

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Critique go4ivy.com 6
This is what they send you 7

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The General Estimation Process (mean, μ , is unknown) Population Random Sample Mean x = 50 I am 95% confident that μ is between 40 & 60. Sample 8
If X N then Z X N ~ ( , ) ~ ( , ) μ σ μ σ 2 01 = - Review – standardization rule 9 - = - = - = ~ ( 0 , 1 ) , ( 1 1 ) 0 . 6 8 ( 1 . 9 6 1 . 9 6 ) 0 . 9 5 ( 3 3 ) 0 . 9 9 7 F o r Z N P Z P Z P Z

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
We construct the interval estimate using the CLT. Recall that the CLT says that X N n ~ ( , ) μ σ 2 10 Then by the Standardization Rule : X n N - μ σ / ~ ( , ) 0 1
We have X n N - μ σ / ~ ( , ) 0 1 Then from what we know about the standard normal distribution: X - μ 11 P n ( . / . ) - < < = 196 196 95% σ -3 -2 -1 0 1 2 3 95% of the area is between –1.96 and 1.96

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
By doing some algebra , we may rearrange stuff so that We have P X n ( . / . ) - < - < = 196 196 95% μ σ 12 P X n X n ( . . ) % - < < + = 196 196 95 σ μ σ truth lower bound upper bound
( 1.96 , 1.96 ) x x n n σ σ - + We are thus 95% confident that the true mean μ is in the interval What does it mean that we are 95% confident ? 13 It means that if we had 100 different samples and created 100 different intervals, 95 out of 100 would contain the true (but unknown) mean.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
What does 95% Confident Mean?
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 50

lect16v4_1up - Stat 104 Quantitative Methods for Economists...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online