Difficulty Levels for Coding Projects: (Easiest = 1 to Hardest = 5)
Project 22: Sampling Distribution of p-hat
Project 23: Sampling Distribution of x-bar
Project 24: Confidence Interval for p
1) Suppose you have to take a 60-question multiple choice test where each question has 5 choices (A,B,C,D,E). You plan on GUESSING on all problems.
a) How many questions will you get correctly on average?
b) What is the standard deviation for the number of questions you will get correctly?
c) Verify that the distribution of possible number of correct answers you will get is approximately normal.
d) What is the probability you answer at least 14 questions correctly?
e) What is the probability you answer less than 11 questions correctly?
f) How many questions would you have to answer correctly to be in the top 10% (aka 90th percentile) in terms of possible questions answered correctly?
2) Savannah household incomes are strongly right skewed with mean $62,000 and standard deviation $33,000. You plan on taking a random sample of 36 households and calculating the mean household income of the sample of households.
a) What is the mean income for the distribution of sample mean incomes? (huh?)
b) What is the standard deviation for the distribution of sample mean incomes?
c) Verify that the distribution of sample mean incomes is approximately normal.
d) What is the probability the mean of your sample is between $60,000 and $70,000?
e) What sample mean income would be in the 80th percentile of possible sample mean incomes?
3) Suppose you took a random sample of 100 Savannah residents and determined that 18 residents had a "house phone". Construct and interpret a 90% confidence interval for the true proportion of Savannah residents that have a "house phone".