BY REBEKAH THOMAS

Confidence Intervals

Confidence Intervals

Intervals that estimate population parameters and margins of error

Estimation is based on sample means or proportions

Example: I am 90% confident that the true average number of calories per cookie is somewhere on the interval (142.87, 150.13).

Confidence intervals for PROPORTIONS

• Margin of error

•Standard deviation

Conditions:1. SRS?

2. Normal?n( )≥10 & n(1 - )≥10

3. Independent?10% rule

z* or t*? Usually t*

If n > 3o and is known, use z*

o If n < 30 or is unknown, use t*

o Remember to use df for t*df = n-1

Confidence Intervals for MEANS

Finding an interval

Calculate a 95% confidence interval for the true average temperature in April for Sandy, Utah.

http://weather-warehouse.com/WeatherHistory/PastWeatherData_Alta_Sandy_UT_April.html

Proportions or means? n = 25 = 34.024 °F S = 3.794 C=0.95

n = 25 = 34.024 °F S = 3.794 C=0.95Check conditions:1. SRS?2. Normal? n≥303. Independent? 10% rule

Use t* since it’s means and st. dev. is unknown.

I am 95% confident that the true average temperature in Aprilin Sandy, Utah is somewhere on the interval (32.458 °F, 35.59 °F).

Interpreting confidence level: 95% of all possible samples of size 25 from the population will result in an interval that captures the true average temperature in April.

Sources

http://sph.bu.edu/otlt/MPH-Modules/BS/BS704_Confidence_Intervals/BS704_Confidence_Intervals_print.html

https://www.google.com/search?q=standard+deviation+symbol&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a&um=1&ie=UTF-8&hl=en&tbm=isch&source=og&sa=N&tab=wi&ei=Out6UemgFsjBrQHm1IGADA&biw=1294&bih=749&sei=Rut6Uf6NLIrlrQGEyIGQAQ#imgrc=_

My notes