FOR INSTRUCTOR'S USE
1. | a........./5 | b........./10 | ........../15 | ||||
2. | a........./5 | b........./5 | c........./5 | d........./6 | e........./6 | f........./8 | ........../35 |
3. | a........./8 | b........./10 | c........./7 | ........../25 | |||
4. | a........./10 | b........./8 | c........./7 | ........../25 | |||
TOTAL | ........../100 |
1. For the following two studies answer the following questions a. Is this an observational study or an experiment? Explain
b. If it is an experiment, define the experimental units,
factor(s), levels of the factors, treatments, and the response variable.
STUDY A.
A researcher advertised for volunteers to
study the relationship between the amount of meat consumed and
cholesterol level. In response to this advertisement, 3476 persons
volunteered. The researcher collected information on the meat consumption
and cholesterol level of each of these persons. STUDY B. Three state governments (Minnesota, Wisconsin, Iowa) wants to investigate whether a job training program helps the families who are on welfare to get off the welfare program. Each state selects 5000 volunteer families who are on welfare and offers the adults in those families free job training. Each state selects another group of 5000 volunteer families who are on welfare and does not offer them such job training. After three years the two groups in each one of the three states are compared in regard to the percentage of families who got off welfare. |
2. Two thousand randomly selected adults were asked if they think they are financially better off than their parents. The following table gives the probabilities that are based on the education level of the persons and whether they are financially better off, the same or worse off than their parents. |
| Better Off | |||
| Same | |||
| Worse Off | |||
a. What is the probability that a randomly selected person is better off? b. What is the probability that a randomly selected person is better off or high school graduate? c. What is the probability that a randomly selected person is better off or worse off? d. What is the probability that a randomly selected person is better off if this person's education level is more than high school? e. What is the probability that a randomly selected person has a less than high school education given that s/he is worse off? f. Are the events "same" and "high school" independent? Are they disjoint? Please justify your answer. |
3. Constantine et al. studied the effects of cranial radiotherapy on brain tumors in children. The distribution of hormonal abnormalities in such children is displayed in the following table (x=number of abnormalities) |
| x | 0 | 1 | 2 | 3 | 4 |
| probability | .10 | .28 | .25 | .25 | .12 |
a. What is the probability that these children will present more than 2 abnormalities? b. Find the mean and the standard deviation. c. If these children present more than 2 abnormalities, what is the probability that there will be 4 abnormalities? |
4. Ms. Thorson lives in Warroad, Minnesota, and drives to the local factory for work at 6:30 a.m. During December, January, and February she is concerned about her truck starting in the morning. When the temperature is below -200F, the probability of starting is 0.30, when the temperature is between -200F and -100F, the probability of starting is 0.60, and when the temperature is -100F or above, the probability of starting is 0.90. The probability of an early morning temperature below -200F is 0.10, between -200F and -100F is 0.30, and -100F or above is 0.60 during these months. a. What is the probability that her truck will start on any given day during this period? b. Given that the car starts what is the probability that temperature is below -200F? c. Given that the car does not start what is the probability that the temperature is -100F or above? |