Goal: To understand and be able to explain what a confidence interval for a proportion really means.
As an individual Scrounge in your pockets or purse and find a legal-tender coin (penny, nickel, dime, quarter, etc.). Toss the coin 20 times and count the number of heads.
What is the proportion of heads that you observed? As natural frequencies: _____ heads in _____ tosses As a proportion: _____ (number between 0.0 and 1.0) As a percentage: _____%
Use your data and (web calculator)_ to calculate a 95% confidence interval for the proportion of heads. 95% confidence interval: _____ to _____ (proportions) or __% to __%
Assuming that you used a fair coin, what proportion of heads would you expect to see if you tossed your coin an infinite number of times? Let's call this the expected proportion. _____ (proportion) OR _____%
Does the 95% confidence interval that you calculated from your data include the expected proportion?
As a group (or pairs or individuals, if necessary, for online class Combine the results of your individual coin tosses. You should have at least 100 coin tosses. If your group is small, you may need to repeat the experiment a few more times.
What is the proportion of heads that you observed? As natural frequencies: _____ heads in _____ tosses (be sure there are at least 100 tosses) As a proportion: _____ (number between 0.0 and 1.0) As a percentage: _____%
Use your group's data and (web calculator)_ to calculate a 95% confidence interval for the proportion of heads. 95% confidence interval: _____ to _____ (proportions) or __% to __%
Is the 95% confidence interval that your group calculated wider or narrower than the one you calculated individually? Why?
Does the 95% confidence interval that your group calculated include the expected proportion?
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coindata <- read.csv("C:\\Users\\telke\\AppData\\Local\\Temp\\RtmpOmqZoX\\datad781d842ab2")
## Warning: incomplete final line found by readTableHeader on
## 'C:\Users\telke\AppData\Local\Temp\RtmpOmqZoX\datad781d842ab2'
coindata
## Timestamp Username Total.number.of.tosses.
## 1 2/15/2013 14:30:55 brea0022@umn.edu 123
## 2 2/15/2013 14:32:25 brea0022@umn.edu 100
## 3 2/15/2013 14:35:11 brea0022@umn.edu 150
## Total.number.of.heads.you.observed. Proportion.of.heads.you.observed.
## 1 34 0.30
## 2 60 0.60
## 3 70 0.48
## Lower.limit.of.your.95..confidence.interval.for.the.proportion.
## 1 0.20
## 2 0.52
## 3 0.40
## Upper.limit.of.your.95..confidence.interval.for.the.proportion.
## 1 0.41
## 2 0.71
## 3 0.70
You can also embed plots, for example:
plot(cars)
