Probability and Inference Test Name

Probability and Inference Test Name:

Review

Standard 9. ComputingProbabilities

Compute probabilities using an appropriate sample space
Compute probabilities using counting rules including permutations and combinations

1.Which of the following is NOT a possible probability?

(a.) 25/100

(b.) 1.25

(c.) 1

(d.) 0

2.When rolling a pair of 6-sided dice, what is the probability of rolling a sum of 6 or 7?

(a.) 1/6

(b.) 3/14

(c.) 5/12

(d.) 11/36

3.Tina has 5 red, 6 blue, 3 white, and 4 orange marbles. All marbles are put in a sack and one marble is selected at random. Compute the probability of drawing a red marble and the probability of drawing a blue or white marble.

(a.) 4/19; 9/20

(b.) 3/10; 11/20

(c.) 5/18; 1/2

(d.) 9/21; 7/18

4.A statistics project was assigned in a class of 20 students. Each student will present his or her work to the class. Three of the 20 students will be selected at random each day to present to the class, and presentations will continue over several days. What is the probability that you and your two best friends in the class will be the 3 students selected to present on the very first day of project presentations?

(a.) 1/1140

(b.) 3/20

(c.) 1/2130

(d.) 2/101

Standard 10. Compound Events

Solve compound probability problems using tree diagrams and area diagrams
Use conditional probabilities – level 1

5.In a basketball one-and-one situation. If a player makes the first foul shot, she gets another foul shot. If she misses it, she does not get to shoot again. (So a player can score 0,1, or 2 points in a one-and-one situation.) Suppose Liz has a 70% chance of making each foul shot. What is the probability that she scores exactly one point in a one-and-one situation?

(a.) 70%

(b.) 9%

(c.) 49%

(d.) 21%

6.A drawer contains 5 black socks and 3 blue socks. If you reach into the drawer without looking and pull out two socks, what is the probability that you get a matching pair?

(a.) 21/56

(b.) 13/28

(c.) 4/56

(d.) 1/2

7.What is the probability that 3 students selected at random were all born on different days of the week? What is the probability that at least two of them were born on the same day of the week?

(a.) 30/49; 19/49

(b.) 36/49; 2/49

(c.) 30/56; 25/36

(d.) 2/3; 1/3

Standard 11. Expected Value

Compute expected value
Make and defend decisions based on expected value calculations

8.Use the table to compute the expected value for X.

X12-3

P(X).3.2.5

(a.)1.2

(b.) 2.5

(c.)-.8

(d.) -2

9.A die is rolled. If the number rolled is odd, Player A wins $2 from Player B. If it is a 6, A wins $4 from B. Otherwise B wins $5 from A. Is this a fair game?

(a.)Yes, because the expected value is 0.

(b.) Yes, because the expected value is positive for player A

(c.)No, because the expected value is negative for player A

(d.) No, because the expected value is 0

10.Refer to Liz’s one-and-one situation in number 5. What is Liz’s expected value for the average number of points she scores in a one-and-one situation?

(a.)1.2

(b.) 2.5

(c.)-.8

(d.) -2

Standard 12. Using the binomial distribution

Graph a binomial distribution
Compute probabilities based on a binomial distribution

11.Which of the following sets of values when substituted into the formula above gives the probability of getting 6 sixes in 10 rolls of a die?

(a) n = 4, p = 10, k = 1/6

(b) n = 10, p = 1/6, k = 4

(d) n = 4, p = 1/6, k = 10

12.Which of the following is not a situation where the binomial probability formula should be applied?

(a.)A coin is flipped 20 times. What is the probability of getting 5 or more heads?

(b.) What is the probability that the first 6 occurs on the 5th roll of a six-sided die?

(c.)What is the probability that Liz will make exactly 3 out of 5 shots if she has a 70% chance of making each shot and we assume independence?

(d.) A bag contains 6 marbles of which two are green. A marble is selected at random from the bag, the color is noted, and the marble is returned to the bag. Repeating this action 15 times, what is the probability of getting 5 or fewer green marbles?

13.The Good Guys have won 60% of their games over a long season. With seven games to go, what is the probability that the Good Guys will win at least five of them? Assume that the Good Guys have a .6 probability of winning each game.

(a.).6

(b.) .36

(c.).42

(d.) .48

Standard 13. Using Normal Distributions

Sketch the graph of a normal distribution
calculate z-scores
Calculate probabilities/proportions pertaining to a normal distribution

Calculate values of a variable corresponding to given probabilities or proportions
Apply the normal approximation to the binomial distribution - level 1 only

14.The distribution of lifetimes for a certain type of light bulb is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. Find the 33rd percentile of the distribution of lifetimes.

(a.) 560

(b.) 330

(c.) 1044

(d.) 1440

(e.) none of these

15.Compute the z-score for a score of 70 on a test with the following summary statistics:

min = 20, Q1 =70, med = 75, Q3 = 76, max = 100, s = 4, = 70

(a) z = 2

(b) z = 2.5

(d) z = 7

16.A negative z-score indicates…

(a) that someone made a computational error

(b) that the mean is a negative number

(d) that the item in question is below the mean

17.A person with a Z-Score of -2.00 has performed below approximately what percent of the students taking the test?

(a) 2 percent

(b) 15 percent

(d) 84 percent

18. In a population there are 60 scores, the mean is 45 and a standard deviation is 25. A score of 85 from this population:

(a.) has a Z-score of 1.60.

(b.) has a Z-score of 1.00.

(c.) has a Z-score of -1.00.

(d.) it is impossible to compute Z without additional information

19.One hundred students took a test on which the mean score was 73 with a standard deviation of 8. A grade of A was given to all who scored 85 or better. Approximately how many A's were there, assuming scores were normally distributed? (Choose the closest.)

(a.) 42

(b.)7

(c.)58

(d.)5

(e.)22

Standard 16. Carrying out statistical tests

Carry out a test of significance (hypotheses, collect and organize data, compute test statistic, compute p-value, make decision, interpret in context)

20.Suppose a medical experiment randomly assigns patients with a certain condition to either receive an “old” treatment or a “new” treatment. The experimenters are interested in whether the new treatment works better than the old treatment. Which of the following would be an appropriate null hypothesis?

(a.)The new treatment works better than the old treatment

(b.)The new treatment works the same as the old treatment

(c.)The old treatment works better than the new treatment

(d.)Neither the old or new treatments work.

21.Medical experimenters randomly assigned 164 pregnant HIV-positive women to receive the drug AZT during during pregnancy while another 160 such women were randomly assigned to a control group which received a placebo. Of those in the AZT group, 13 had babies who tested HIV-positive, compared with 40 HIV-positive babies in the placebo group. Contruct two-way tables of observed and expected counts. If there is no difference between AZT and the placebo, what number of babies of mothers in the control group would be expected to be HIV positive?

(a.) 26.2 (b.)19.3

(c.)40(d.)13

22.In an experiment to study attempting to identify factors which can influence people’s responses to survey questions, subjects were randomly given one of the two following statements and asked whether they agree or disagree:

A: “Individuals are more to blame than social conditions for crime and lawlessness in this country.”

B: “Social conditions are more responsible than individuals for crime and lawlessness in this country.”

Blame Individuals / Blame Social Conditions / Total
A / 282 / 191 / 473
B / 204 / 268 / 472
Total / 486 / 459 / 945
Statistic / DF / Value / P-value
Chi-square / 1 / 25.4347 / <0.0001

The responses are summarized below:

Which of the following is an appropriate conclusion for a chi-square test of the null hypothesis that the wording of the question did not influence the responses:

(a.) Accept the null hypothesis. There isn’t sufficient evidence to demonstrate that the wording of the question had an effect.

(b.)Reject the null hypothesis. There is strong evidence that people were influenced by a tendency to agree with the researcher

(c.)Fail to reject the null hypothesis. People were more likely to disagree than to agree with whichever statement was given.

(d.)Reject the alternative hypothesis. There no evidence suggesting that the wording of the question influenced responses.

Standard 17. Understanding Statistical Tests

Explain p-value as a probability
Understand the reasoning for a test of significance

23.Which of the following is the best explanation of a null hypothesis, Ho, in a statistical test.

(a) a statement of what we are trying to prove in an experiment

(b) it is usually a statement that “there really is a difference”

(c) a neutral assumption made for the sake of argument that the researcher tries to disprove based on conflict with the observed data

(d) it is the hypothesis that the data cannot be explained by random variability

24.A p-value of 0.11 would indicate…

(a) that someone made a computational error

(b) strong evidence against the null hypothesis

(d) that we should fail to reject the alternative hypothesis at a .05 significance level

25.Roberto suspects that his brother’s coin is biased towards heads. He flips the coin a large number of times and records the results. Suppose that the number of “heads” he got differs from the expected number of “heads” from a fair coin so much that the p-value in a Chi-square test is 0.04. Which of the following is not a correct interpretation of this p-value?

(a) In only 4 random samples in one hundred would we see such a large difference between the observed and expected numbers of heads when flipping a fair coin

(b) The null hypothesis of the test is rejected at the .05 significance level

(d) If Roberto’s brother’s coin is fair, the probability of observing such a large difference between the observed and expected numbers of “heads” is fairly small.

26.It is appropriate to reject the null hypothesis in a test of significance if…

(a) it would be very unlikely to get the sort of data that was observed if the null hypothesis were true.

(b) the data are consistent with what would be expected if the null hypothesis were true

(d) the chi-square value is close to 0

Standard 18. Computing confidence intervals

Compute and interpret a confidence interval

27.Based on a random sample of 400 American drivers, survey participants were asked if they routinely use a cell phone while driving. A 95% confidence interval based on the collected data was .55 to .61.Which of the following is the best interpretation of this interval?

(a) Between 55% and 61% of drivers in the sample use a cell phone while driving

(b) With 95% confidence, the proportion of all American drivers who use cell phones is estimated to be between 55% and 61%

(d) We are 95% confident that the true proportion is in this interval 95% of the time

28.In a random sample of 200 Havertown residents, 120 said that they support constructing a new library at the site of the old bubble gum factory. Compute a 95% confidence interval for the true proportion of all Havertown residents who support the new library.

(a) 57% to 65%

(b) 33% to 49%

(d) 42% to 53%

29.The formula for a confidence interval is where z* corresponds to the desired confidence level. What value of z* would be used for a 92% confidence interval?

(a) .92

(b) 1.19

(d) 1.75

Standard 19. Understanding Confidence Intervals

Understand the Central Limit Theorem
Explain what is meant by statistical confidence relating to a confidence interval

Understand the relationship between sample size, confidence level, and width of interval (or margin of error)
Distinguish between practical significance and statistical significance - level one only

30.A 95% confidence interval estimate for a population proportion was computed with a margin of error of 9%. Using a larger sample size for such a 95% confidence interval would result in an interval which is…

(a) more narrow

(b) more wide

(d) sample size has nothing to do with the width of the confidence interval

31.Which set of circumstances is most likely to result in a narrowconfidence interval?

(a.) large n and a confidence level of .95.

(b.) large n and a confidence level of .99.

(c.) small n and a confidence level of .95.

(d.) small n and a confidence level of .99.

32.In repeated samples and constructions of 99% confidence intervals for apopulation proportion, which of the following is the best explanation of statistical confidence?

(a.) The true proportionfalls in eachof these intervals approximately 99% of the time.

(b.) After we collect a sample and compute the confidence interval, we can say that there is a 99% chance that thetrue proportion is in the interval

(c.) 99 out of a 100 populations will have their population proportions in theinterval.

(d.) 99% of the intervals computed will contain the sample proportion

33.Since the distribution of sample proportions is approximately normal, based on the empirical rule, we can say that …

(a.) about 95% of population proportions are within 3 standard deviations of the mean

(b.) about 95% of sample proportions will be within 2 standard deviations of the true proportion

(c.) about 95% of the time, the true proportion is the mean of the sampling distribution

(d.) about 95% of confidence intervals successfully capture the sample proportion

Standard 20. Experimental Design

Understand principles of control including comparison, replication, randomization, blindness, and blocking
Carry out a well-controlled experiment

34.What is the role of randomization in an experiment?

(a.) A random sample of subjects is selected from a population to avoid bias

(b.) Subjects are randomly assigned to treatments so create experimental groups that are similar

(c.) Treatments are applied to every subject at random intervals

(d.) Experimenters must randomly decide what the purpose of the study is

35.The control group in an experiment should be designed to receive:

(a.) the opposite of the experiences afforded the experimental group.

(b.) the same experiences afforded the experimental group except for the

treatment under examination.

(c.) the experiences afforded the experimental group except for

receiving the treatment at random intervals.

(d.) the experiences which constitute an absence of the experiences

received by the experimental group.

36.In an experiment to see if Smartfood Popcorn makes people smarter, 50 students are randomly assigned to two groups. The first group receives Smartfood popcorn and the second gets regular popcorn. Then each student writes an essay on an assigned topic. The essays are scored by a teacher and the results are compared for the two groups to see if Smartfood had a positive effect on essay writing. Which of the following would ensure blindness and double-blindness in this study?

(a.) the students and reseachers should both wear blindfolds

(b.) no one should know whether Smartfood was used for either group.

(c.) the students should not know whether they got Smartfood or a different brand of popcorn, and the teacher should not know which group the the student was in while grading the essay.

(d.) Smartfood should be given to both groups but in random intervals so that the students do not know when they are getting it

Standard 21.Studies

distinguish between explanatory and response variables
distinguish between observational studies andexperiments
understand when a "cause and effect" conclusion is justified
understand and identify lurking (confounding) variables

37.An experiment is conducted to determine if the use of certain specified amounts of a drug will increase IQ scores. In this study, IQ serves as:

(a) an explanatory variable

(b) a moderator variable

(d) a control variable

38.In order to test the effects of light level on student performance on tests, subjects are randomly assigned to two rooms to take a test. One room had a lower light level than the other. During the testing it was noted that one room’s temperature was 70 degrees whereas subjects in the other group are simultaneously tested in a nearby identically appointed room with the heat set at 60 degrees. A possible confounding variable in this study is…

(a.) test score

(b.) lighting level

(c.) temperature

(d.) random assignment

39.Researchers would like to understand how pet ownership is related to longevity. Which of the following is true?

(a.) This study would be considered an observational study if they randomly assigned subjects to either receive a pet or not.

(b.) This study would be considered an experiment if they randomly assigned subjects to either receive a pet or not.

(c.)This study would be considered an experiment if they took a random sample of pet owners and noted whether or not they owned a pet

(d.) none of the above is true

40.If the researchers in a study want to be able to conclude that watching television CAUSES poor academic performance and is not merely ASSOCIATED with school performance they need to…

(a.) Conduct a well-controlled experiment

(b.) Use an unbiased random sample in an observational study

(c.) both (a.) and (b.) would be appropriate studies for the researchers

(d.) neither of these types of studies can be used to establish a cause-and-effect relationship between watching TV and academic performance