Supplies: 1 scoop of conversation hearts per student (about 50).
1. Do not eat the hearts until this activity is completely finished. Separate by color. Count and record how many of each color and your total sample size.
2. What proportion of hearts are pink in your sample?
3. Do you know the proportion of pink hearts in the original population?
4. Did everyone in class obtain the same proportion of pink hearts?
5. Find the mean of the proportions for the class.
6. If you wanted to predict the true proportion of pink hearts manufactured, what could you do to increase the accuracy of your prediction?
7. Suppose each person in class calculated a 95% confidence interval for the true proportion based on his/her own sample. What percentage of the confidence intervals would you expect to contain the true proportion?
8. What type of distribution is described by counting how many hearts
are pink and how many are not pink, in a given sample?
9. Open your book to p. 382 (IPS). Find the green heading:
"Normal approximation for counts and proportions". Start reading
there and read through p. 385.
a. If n is large, what distribution does a binomial distribution approximate?
b. How big must n be so that you can use this approximation? (Read the paragraph in the middle of p. 587.)
c. Were you provided with a large enough sample
size to use this approximation? Base your answer on the mean of the
proportions for the class.______ How big a sample size would be needed?_______
10. Go to your distant past and find the method for calculating the
standard deviation for:
a. a proportion from a binomial distribution. Perform the calculation based on your sample.
b. a count from a binomial distribution. Perform the calculation based on your sample.
11.You want to obtain a 95% confidence interval for the true proportion
of pink hearts, based on your sample.
a. What do you need to know to calculate a confidence interval for your sample? Refer to your past experiences with
confidence intervals in formulating your answer.
b. Calculate the confidence interval for your sample.
12. Make the longest possible sentence using the words on your conversation hearts. Write it here.
BOOK HOMEWORK: Read Introduction to the Practice of Statistics p. 586-592. Do problems on p. 596 #1-8.