I will be having a test in my statisitics class but my teacher is HORRIBLE and we dont seem to have any tutors for this subject material... So i was hoping some one could give me some answers and explain them so when the test comes I will have some idea of what i am doing.
This is my study guide and i have also taken the liberty to list the formlas we are using - any help greatly would be appreicated!
Let’s say the Jelly Belly company produces equal numbers of jelly beans in each of ten colors. Each bag contains a sample of jelly beans from the total produced by the company. Say the jelly beans are sold in three different quantities: a frustratingly tiny bag for vending machines, a larger bag sold at pharmacies, and a very large Halloween sized bag. Some people really hate black jelly beans, and will be frustrated if a large percentage of the jelly beans in the bag they buy happens to contain a large percentage of black jelly beans. Say the jelly beans in each bag are randomly chosen.
1. What size of bag should someone buy if they are a risk-taking hater of black jelly beans, willing to risk getting a bag with a high percentage of black ones, for the opportunity to get a bag with a small percentage of black jelly beans?
2. Explain your answer for #1
3. Let’s say another person has different preferences. They are interested in dieting, and have interpreted this to mean they must have a balanced diet in jelly beans. What size of bag is most likely to provide a "balanced diet" of jelly beans?
4. Explain your answer to #3.
5. What concept in statistics should be illustrated by your answers to the previous questions?
6. A jelly bean fiend buys a new large bag every day, and counts up and records the number of beans of each color before consuming rapidly. At the end of a year, the fiend has a record of 365 samples of 300 jelly beans each, and one tooth left. He proceeds to record the proportion of the coveted red jelly beans for each of the 365 samples. He draws a histogram of the distribution of all of these proportions. What is the technical term for this distribution?
7. What is the shape of the distribution for question #6?
8. What idea in statistics is responsible for the result of #7?
9. There is a special name for the standard deviation of the distribution named in question #6. What is it?
10. Unlike the fiend described above, most people only buy a large bag of jelly beans once in a while. Can these people estimate the proportion of jelly beans of any particular color? Yes, as long as the bags of jelly beans are a random sample from the total produced. Say a person counts 27 red in a bag of 300 beans. Estimate the 95% confidence interval for the proportion of red beans produced by the company.
a. First, estimate the standard error.
b. What is the standard error a measure of?
c. What is the z-score associated with the 95% confidence level?
d. What is the lower bound?
e. What is the upper bound?
11. What is the 99% confidence interval for the proportion of red beans produced by the company?
Confidence interval for a proportion =
Lower bound: p – z*standard error
Upper bound: p + z*standard error
p = proportion.
-z = norminv((1-confidence level)/2, 0, 1)
Standard error = standard deviation / sqrt(n) where n = sample size.
Standard deviation for a proportion = sqrt(p*(1-p))