Midterm Review and Practice
I. Correlation -
Practice Problem
1. Open
the file
a. Make a XY scatterplot of gestation vs. average longevity. Include a trendline (no equation) and the correlation coefficient.
b. Open CriticalValuesForR.xls. Is the relationship between gestation time and average longevity statistically significant?
c. Discuss the strength (strong, positive or weak) of the relationship between these two variables. Also discuss whether the relationship is positively or negatively correlated.
d. Are there any outliers in this dataset? What are they? Are there any benefits to removing the outliers? Are there any negatives to removing the outliers? What might you do in this case?
e. Does a longer gestation time cause an animal to live longer?
II Probability -
Basic Rules to Know:
The probability of an event is between 0 and 1. A probability of 1 is equivalent to 100% certainty.
If the probability of an event A is pr(A), then the probability of event A not occurring is
pr(not A) + pr(A) = 1 OR pr(not A) = 1 - pr(A)
If two events A and B are independent (this means that the occurrence of A has no impact at all on whether B occurs and vice versa), then the probability A and then B occurring is
pr(A and B) = pr(A)×pr(B)
If two events A and B are mutually exclusive (this means A cannot occur if B occurs and vice versa), then the probability of either A or B occurring is
If two events are not mutually exclusive (meaning A and B could happen together), you must subtract the probability that A and B do happen at the same time.
pr(A or B) = pr(A) + pr(B) – pr(A and B)
Practice: See Probability Worksheet and Activities 2 and 3.
More probability practice:
1. When flipping a coin 5 times what the probability of getting...
5 heads in a row?
4 heads and then a tail?
exactly one tail?
at least one tail?
2. In our class of 27 students, there are 20 females and 7 males. Of all the last names, 6 end with a vowel and the rest end with a consonant. There are 5 females with a last name ending in a vowel. Fill in and complete the following table and then answer the questions.
| Female | Male | Total | |
| ends in vowel | |||
| ends in consonant | |||
| total |
What is the probability that a randomly chosen person from the class...
is a male?
has a name that ends in a consonant?
is a female whose name ends in a consonant?
is either a male or has a name that ends in a vowel?
3. Suppose you have to cross a train track on your commute. The probability that you will have to wait for a train is 0.20. If you don't have to wait, the commute takes 15 minutes, but if you have to wait, it takes 20 minutes.
i. What is the expected value of the time it takes you to commute?
ii. Is the expected value ever the actual commute time? Briefly explain.
4. To quote Forrest Gump, "My momma always said, 'Life was like a box of chocolates. You never know what you're gonna get.'" You have a box of 20 chocolates with 8 creme caramel, 5 dark chocolate truffle, 4 coconut almond, and 3 mint.
What is the probability that if you close your eyes a pick one chocolate, that it is a:
dark chocolate truffle?
not a coconut almond?
either a mint or a creme caramel?
You hate coconut almond. What is the probability that if you randomly pick a chocolate, taste it, put it back and pick another one, that they both would be coconut almond?
If you pick 5 (and return after one taste), what is the probability that at least one of them is the dreaded coconut almond?
5. Insurance companies use the concept of expected value to determine how much to charge their customers. customers pay for insurance coverage. If there is a claim made, the company must pay the customer. An insurance company charges one customer $500 for its policy for one year. There is a 10% probability that the customer will make a claim for $2500 which the insurance company will have to pay out. There is a 20% probability that the customer will make a claim $1000 (This means there is a 70% probability that the customer will make no claim).
a. What is the expected value for how much the company will pay out to the customer?
b. Is the company expected to make money on that policy? Explain
6. Redo Homework 2
NOTE: From our last lecture, expected value, gambler's fallacy, confusion of the inverse, Simpson's paradox, coincidences, and risk/relative risk will be covered on the midterm. Descriptive Statistics will NOT be covered on the midterm.