1. Should you have a cup of coffee to make you more alert when studying for a big test? A researcher is interested in studying the effect of caffeine, and he comes up with the following plan for an experiment. The experiment will involve 100 volunteers each of which will take a memory test 20 minutes after drinking cola. Some volunteers will be randomly assigned to drink caffeine free cola; some to drink regular cola (with caffeine), and others a mixture of the two (getting a half dose of caffeine). For each volunteer, a test score (the number of items recalled correctly) will be recorded. The volunteers will not be told which type of cola they receive, but the researcher who evaluates the results will prepare the cups of cola right on the spot (out of sight of the volunteers).
For parts (a) to (e), choose the correct answers from the following list:
A. a glass of cola
B. a volunteer
C. a blocking variable
D. a response variable
E. a confounding variable
F. a factor
G. caffeine--free cola and regular cola
H. no caffeine, half dose of caffeine and full dose of caffeine
I. completely randomized design
J. random block design
a) What is the experimental unit?
b) Caffeine is
c) The treatments are
d) The results of the memory test is
e) What type of design is this experiment?
f) True or False? The experiment is double--blind.
True False
g) The exam room only holds 50 people so one exam was run in the morning while the other was run in the afternoon. Describe the levels of the variable "exam time" and what type of variable it is in the context of experiments.
2. Lack of regular exercise is a growing problem in North America. A survey is to be done to determine the proportion of Canadians that don't get the proper amount of exercise needed for a healthy life style.
a. Describe a Multistage Sampling procedure that stratifies on two variables that could be recommended here. Make an argument for stratifying on these variables.
b. 45% of Canadians don't exercise enough. Suppose that in a simple random sample of 1000 adults 51% of respondents don't exercise enough.
i. The value 45% is a (check one)
parameter
Statistic
ii. Fill in the blanks and show your calculations (no need for verification of conditions) [
There is a 95% chance that in a random sample of size 1000, the sample proportion of Canadians who don't exercise enough will be between % and %
iii. If we decide to decrease to 90%, then the width of the interval will (choose one)
Become wider
Remain the same
Become narrower
Not enough info to tell
3. The distribution of incomes of people in Northern BC is skewed to the right with mean $47,512 and standard deviation $20,000.
a) Consider selecting one of all possible samples of size 400 that can be drawn from all Northern BC residents.
i. What type of sampling would this be [1 mark]:
· Simple Random Sampling
· Stratified Sampling
· Cluster Sampling
· Multistage Sampling
ii. The sampling distribution of the sample mean income for random samples of size 400 is skewed to the right because these incomes have a distribution that is skewed to the right. approximately normal because the sample size 400 is sufficiently large. exactly normal because the sample size 400 is sufficiently large. b) There is approximately a 95% chance that the sample mean income of a random sample of 400 residents of Northern BC will fall between $45,512 and $49,512.
True False
c) The proportion of all residents of Northern BC which earn over $100,000 in yearly income is a parameter.
True False
d) Suppose the percentage of all Residents in Northern BC who earn over $100,000 is 8%. A random sample of 400 individuals is to be chosen. What is the probability that less than 10% of the sample will be people who earn over $100,000?
e) If the researcher increases the sample size to 1000, then the probability that less than 10% of the sample will earn over $100,000 will ... (circle one)
i. Increase
ii. Remain the same
iii. Decrease
iv. Not enough info to tell
4. In a school of 1000 students, 45% of students refused to get vaccinated for H1N1. The other students were all vaccinated. In all 17.1% of students were attained by H1N1 (after vaccination). Of the infected students, 23 had been vaccinated.
a) What is the probability that a student in this school will have not been vaccinated and infected?
b) What is the probability that they have either been vaccinated or infected (this includes the possibility of having both)? In other words what is the probability they have antibodies?
c) What is the probability that someone who was infected was vaccinated?
d) Are the events "Being Vaccinated" and "Contracting H1N1" independent? Justify your answer with some calculations.
e) Are the events "Being Vaccinated" and "Contracting H1N1" disjoint? Justify your answer.
5. A recent study that examined video game playing among fourth to sixth graders shows a clear association between time spent playing video games and later violent behaviour. A parent reads about the study and concludes that video games cause more violent behaviour. Do you agree with this parent? Explain your reasoning.