2. A cohort study investigated the relationship between cholesterol levels and the risk of coronary heart disease. Investigators studied 250 people at high risk for heart disease between the ages of 50-59, following them for 10 years. A hundred people were on a low cholesterol diet compared to 150 people on a high cholesterol diet. After 10 years the number of people who had coronary events were recorded and coded as heart disease (yes vs no). The SAS table output below summarize the findings. Based on this table answer the following questions:
a. What percentage of individuals who had heart disease were on a low cholesterol diet?
b. What percentage of individuals who ate a high cholesterol diet had evidence of heart disease?
c. What is the odds of heart disease among those on a low cholesterol diet?
d. What is the odds of heart disease among those on a high cholesterol diet?
e. What is the odds ratio for the risk of heart disease among those on a high cholesterol diet compared to a low cholesterol diet?
3. When I visit the local library, the probability that someone is reading the current issue of US is 0.4, the probability that someone is reading Time is .3, and the probability that at least one is being read by someone is .5.
a) I am planning on going to the library and taking both of them immediately. What is the probability that both magazines are being read?
b) What is the probability that neither of the two is being read?
c) What is the probability that exactly one is being read?
4. Suppose that in a city 37% of the voters are registered Democrats, 29% are registered Republications, 11% are members of other parties (e.g Green party etc) and the remaining are not aligned with any party, called Independents.
a. What is the probability a single randomly selected person from this city is an Independent voter?
b. Suppose you conduct a poll by calling 5 randomly selected registered voters, what is the probability that exactly three are Republicans? (hint: Binomial)
c. What is the probability of no Democrats out of 5 randomly selected registered voters?
d. What is the probability of at least one Independent voter out of 5 randomly selected registered voters? (hint: Binomial)
e. Suppose a polling organization calls 1000 registered voters, how many on average do we expect to be Independent voters?
e. Suppose a polling organization calls 1000 registered voters, how many on average do we expect to be Democratic voters?
5. 56% of all American workers have a workplace retirement plan, 68% have health insurance and 49% have both benefits. We select a worker at random
a. What is the probability that they have neither plan (health insurance nor retirement)
b. What is the probability they have either health insurance or a retirement plan?
c. What is the probability they have ONLY a retirement plan?
d. Are having a retirement plan and a health insurance plan mutually exclusive? Explain.
e. Are having a retirement plan and a health insurance plan independent? Explain.
6. A soft drink company holds a contest in which a prize may be revealed on the inside
of the bottle cap. The probability that each bottle cap reveals a prize is 0.2, and
winning is independent from one bottle to the next. You buy three bottles. Let X= number of winning bottles out of 3 tries
(a) What is the sample space of X? In other words, what are all the possible values of X that you could see?
(b) Find the probability that none of your bottles reveals a prize.
(b) Find the probability that exactly 1 of your bottles reveals a prize.
(c) Find the probability that you win at least one prize.
(d) Can X be considered arising out of a Binomial distribution? If so what are n and π? And list all the characteristics that makes it compatible with this type of probability distribution.