Mth 243 Introduction to Statistics

Mth 243 Introduction to Statistics Exam 2 Review

1. A researcher conducts a study to determine whether underage drinking affects academic performance in college. She randomly asks 100 “under 21” students if they have consumed alcoholic beverages at least once a month during the term. She then compares the GPA of students who have been drinking with those who have not. a. Is the study an experiment, observational study, or survey? b. Is the sample a SRS, stratified sample, cluster sample, systematic sample, convenience sample, or voluntary response sample? c. Two types of bias that may occur are: “response bias” and “undercoverage”. Which of these are potentially a problem in this study and why. study.

2. On election day Americans will be eager to hear the results of “exit polling”. In this type of poll, as voters come out of the voting booth (not possible in Oregon!) they are asked how they voted. In past elections, exit polls have been biased. They over estimated the percent of the vote received by candidates of color. What type of bias is this? Why does it occur?

3. A recent Mth 243 research team wished to compare the worm population in a field that had been plowed repeatedly over several years with the worm population in a field that had not been plowed in recent years. Their plan was to weigh the amount of worm material that is in a core sample of dirt. 1. Is the study an experiment, observational study, or survey?

2. What are the “individuals” in this study?

3. Identify the explanatory and response variables? What type of variables are each?

4. The worm research team (above) considered four different options for sampling: SRS, Stratified Sampling, Cluster Sampling, and Systematic sampling. They placed a grid over a map of the rectangular field with each “box” created by the grid representing a potential sampling spot. Identify each of the four types of sampling the group might use.

a. Randomly select a column and a row, collect the sample, and then repeat. b. Start with the first row, randomly select two areas in the row. Collect a sample from each of the two areas Move to the next row and repeat. c. Randomly select an area in the first row, Collect sample. Skip 4 areas and sample the fifth. Skip another 4 areas and sample. Repeat. d. Randomly select a row and column to identify an area. Collect samples from all adjacent areas. Repeat.

5. An industrial psychologist is interested in studying the effect of room temperature and humidity on the performance of tasks requiring manual dexterity. She chooses three temperatures of 65 degrees Fahrenheit, 80 degrees Fahrenheit and 95 degrees Fahrenheit with humidity of 60% and 80%. She plans to measure the number of correct insertions, during a 15- minute period using a peg-and-hole apparatus requiring the use of both hands simultaneously. After each subject is trained on the apparatus, he or she is asked to make as many insertions as possible in a 15-minute period. Sixty factory workers from each of three different companies are to be randomly assigned to the different temperature and humidity combinations.

a. Identify the population under study. b. Identify the “individuals” units in this experiment. c. How many factors are there? d. How many treatments? e. What blocking variable(s) are reasonable?

6. A group of statistics students is interested in whether drinking herbal tea helps seniors in an assisted living home feel better. They visit a home and serve herbal tea every day for a week to a randomly selected group in the home. At the end of the week, the nursing supervisor interviews each person who received tea and scored them on a scale of 1 to 10 (feeling much better). She reported the result to the team.

This is not a comparative random experiment. Identify the problems this study has.

Design a comparative random experiment that would best solve these issues. 7. Imagine a jar full of marbles. Each marble in the jar is red, blue, green, or yellow. a. Which of the following are valid probability distributions of the colored marbles? Explain why the probability distribution is valid or not.

Color Red Blue Green Yellow Probability .1 .3 .5 .1

Color Red Blue Green Yellow Probability .3 .3 .3 .3

b. Create a probability distribution for a jar of marbles in which there are no yellows, the same number of blue and green, and more reds than all the others combined.

8. Identify the type of probability for each scenario: a. You pull out of the jar 20 marbles and count 5 of them as red. You claim the probability is .25 of selecting a red marble from the jar. b. You put 250 red marbles in a large jar along with 750 green marbles. You claim the probability is .25 of selecting a red marble from the jar. c. You are told that if you draw a red marble from a jar full of marbles that you will win $1000. Since you are unlucky you claim the probability is .25 of selecting a red marble from the jar.

9. At a party there is a jar with 500 red marbles, 1000 green marbles, 10 blue marbles, and 490 yellow marbles. Every time you select a marble from the jar you note the color, replace it in the jar, and then re-mix the marbles. a. If you play the game a large number of times what percent of the time would you expect to draw out a blue marble? b. Imagine that you will be paid $1000 if you select a blue marble, $4 for red or yellow, and you lose $5 for selecting a green. However, it will cost you $5 each time you select a marble. How much would you expect to win or lose in the long run?

10.Using a standard normal probability distribution with mean zero and standard deviation 1, find the following probabilities (draw a sketch of each). a. P(z<1) c. P(z>-2) b. P(-1.64

12.Suppose that the age of student cars is not normally distributed. Under what conditions is the sampling distribution of sample means distributed normally.

13.A tavern claims that the average pint of beer they serve is indeed a pint, i.e. 16 oz with a standard deviation of 1 oz. You investigate by measuring (and sampling) 49 “pints”.

a. What would be the sampling distribution for x with sample size 49?

b. Your sample mean turns out to be 15.6 oz. What would you conclude and why?