psych 311 study guide

What values are distributed along the x-axis for a sampling distribution of the sample mean? A) scores B) sample means C) sample variances D) both B and C

B

86. The ________________________________________theorem explains that the shape of a sampling distribution of sample means tends toward a normal distribution, regardless of the distribution in the population

central limit

14. Probability ranges between 0 and 1 and is never negative. A) True B) False

A

What are three ways that the standard error is reported in research journals?

Reporting SEM in the text Reporting SEM in the table Reporting SEM in the graph

The sample space is equal to the total number of random outcomes possible for a random variable. True False

a

The central limit theorem states that the sample mean will equal the population mean on average. True False

B

A researcher selects a sample of 625 participants from a population with a mean of 120 and a standard deviation of 25. The probability of selecting a sample mean that is larger than 125 is close to zero. True False

A

The sampling distribution of the mean has minimum variance. True False

A

The sampling distribution of the mean is a distribution of all the possible samples of a particular size that can be selected from a given population. True False

A

19. A binomial probability distribution is constructed for random variables that have at least two possible outcomes. A) True B) False

B

77. For the experimental sampling strategy, A) the order in which a participant is selected matters B) sampling is with replacement C) sampling is without replacement D) participants are not sampled from the population, but instead are sampled from other samples already drawn

C

How many possible samples of size 2 can be selected from a population of 5 using theoretical sampling? A) 5 B) 10 C) 25 D) 32

C

74. Regardless of the shape of the distribution in the population, the sampling distribution of sample variances approximates a A) normal distribution B) positively skewed distribution C) negatively skewed distribution D) multimodal distribution

B

A researcher selects a sample of 9 participants from a population with a mean of 8 and a standard deviation of 3. About 14% of the sample means in this sampling distribution should be between a sample mean of 6 and 8 5 and 6 9 and 10 10 and 11

C

Bayes' theorem is often applied to a variety of ________ probability situations, including those related to statistical inference. A) generic B) absolute C) conditional D) fixed

C

Most behavior is believed to ________ a normal distribution. A) be exactly equal to B) not resemble at all C) approximate

C

Explain why the sample mean is an unbiased estimator (i.e., what does that mean and how can you check it mathematically?)

it means the sample mean equals the value of the population mean on average

A professor records the grades for his class of students. He finds that the probability that a student earns an A is p = .14; earns a B is p = .36; earns a C is p = .32; earns a D is p = .10; and earns an F is p = .08. What is the probability that a student earns a B or better in this class? .36 .14 .86 .50

.5

17. The expected value of a random variable is the mean of a probability distribution. A) True B) False

A

41. The sample mean is an unbiased estimator of the population mean. A) True B) False

A

47. There are 25 possible samples of size 2 that can be selected from a population of 5 people using theoretical sampling. A) True B) False

A

A researcher selects from a participant pool of 4 males and 6 females. He determines that the probability of selecting 2 male participants is p = .16. Based on this probability, what strategy did the researcher use to sample participants. sampling with replacement sampling without replacement

A

For a set of data with 25±2.5, at least 95% of scores fall between 20 and 30. True False

A

How is the standard error of the mean typically reported in a graph? A) using error bars B) by plotting sample means C) by listing group names along the x-axis D) it is never reported in a graph

A

Probability distributions display the probability of each possible outcome for a given random variable. True False

A

The average sample variance equals the population variance when dividing SS by df. A) True B) False

A

The binomial probability distribution is distributed with u=np, and o=square root npq . A) True B) False

A

The mean of the sampling distribution of sample means is A) equal to the population mean B) equal to the population variance C) both A and B D) none of the above

A

A researcher selects a sample of size 6 from a population of size 10. How many possible samples of this size can be selected using theoretical sampling? A) 100,000 B) 1,000,000 C) 10,000,000 D) over 60,000,000 samples

B

A researcher states that a sample of 100 shoppers spend 112 ± 40 (M ± SEM) dollars on groceries each week. Which value is the standard error of the mean? 112 40 100 The standard error of the mean is not reported in the article

B

A researcher wants to know the probability of being named on the honor roll from a population where 8% of students are on the honor roll. If the researcher selects a sample of 400 students, then what is the mean number of students expected to be on the honor roll? Hint: This is a binomial distribution, where p = 0.08 and q = 0.92. 29 32 368 200

B

As sample size increases, the standard error of the mean increases decreases can increase or decrease does not change

B

In a normal distribution a score of 8 will always be more probable than a score of 0. True False

B

Give an example of two outcomes that are complementary (i.e., their probabilities are complementary

flipping a coin choosing out of a population

Define the central limit theorem

given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.

A _______________ distribution of the sample means is a distribution of all possible sample means that can be obtained in samples of a given size (n) from a population (N).

sampling

30. A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called A) a conditional procedure B) a sampling distribution C) sampling without replacement D) random sampling

B

70. Scores far from the mean are located in the ________ of a normal distribution. A) body B) tails C) most sensitive areas D) most uncertain areas

B

A researcher determines that the probability of missing class among students at a local school is p = .16. Assuming that the school has 300 students enrolled, how many students can we expect to miss class on a given day? Hint: This is a binomial probability distribution. 252 students 48 students 16 students There is not enough information to answer this question.

B

A researcher reports that the probability of a college student living on campus is p = .38. If a small local college has 2,000 students enrolled, then what is the standard deviation of college students living on campus? Hint: This is a binomial probability distribution. 471.2 students 21.7 students 760 students There is not enough information to answer this question.

B

Each of the following statements are true, except that A) increasing the sample size will decrease standard error B) the larger the sample size, the larger the standard error C) the larger the standard deviation in the population, the larger the standard error D) both B and C

B

If a researcher selects a sample of 64 participants from a population with a variance of 16, then the standard error of the mean will be 2.0. True False

B

The probability of an outcome is particularly useful for predicting the likelihood of fixed events. True False

B

What is the z score for scores in the bottom 5%? A) 1.645 B) -1.645 C) .4801 D) -0.050

B

If the standard deviation of a probability distribution is 9, then the variance is A) 3 B) 9 C) 81 D) unknown

C

The mean of a probability distribution is called the A) expected value of the mean B) mathematical expectation C) both A and B D) none of the above

c

The probability of a college student being employed is p = .35. The probability of a student being employed and dropping out of college is p = .20. Hence, the probability of a student dropping out of college, given that he or she is employed, is p = .07 p = .57 p = .55 There is not enough information to answer this question.

B

What is the implication for the tails of a normal distribution being asymptotic? A) that scores above the mean are distributed the same as scores below the mean B) that extreme scores are possible in a normal distribution C) that there are an infinite number of possible normal distributions D) that this characteristic has no practical implication

B

Which proportion is largest in a z distribution? A) The proportion of area above the mean. B) The proportion of area between z = +1 and z = -1. C) The proportion of area greater then z = 1.0. D) The proportion of area less than z = 0.

B

Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities? additive rule multiplicative rule both A and B none of the above

B

A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20. About 68% of the sample means in this sampling distribution should be between a sample mean of A) 34 and 40 B) 34 and 38 C) 38 and 44 D) 36 and 40

D

Each of the following is an example of a binomial distribution, except A) the number of heads in ten flips of a fair coin B) the number of males and females in a sample C) the number of votes for or against a candidate D) the time it takes to complete a driving test

D

In a normal distribution, 50% of all data: fall above the mean fall below the median fall above and below the mode all of the above

D

What is the z score for scores in the bottom 10%? A) 1.28 B) 2.32 C) -2.32 D) -1.28

D

A binomial probability distribution is the distribution of random outcomes for a bivariate or dichotomous random variable. True False

A

A researcher selects a sample of 16 participants from a population with a variance of 4. What is the standard error of the mean? A) less than 1 B) equal to 1 C) greater than 1 D) There is not enough information to answer this question.

A

A researcher selects a sample of size 4 from a population of size 6. How many possible samples of this size can be selected using experimental sampling? A) 15 B) 30 C) 1,296 D) 4,096

A

Assume number of days absent is normally distributed. If a sample mean is 8 and SD is 2, what's the z-score for a person with 2 days absent? -3 -2 3 99

A

The normal distribution is symmetrical, which means that A) scores above the mean are distributed the same as scores below the mean B) extreme scores are possible in a normal distribution C) there are an infinite number of possible normal distributions D) this characteristic has no practical implication

A

The probability that a participant is married is p(M) = .60. The probability that a participant is married and "in love" is p(ML) = .46. Thus, the probability that a participant is in love, given that the participant is married is p = .77. True False

A

The standard error of the mean is the standard deviation in a sampling distribution of sample means. True False

A

The standard normal distribution is normally distributed with a mean of ____ and a variance of ____. 0; 1 1; 0 any value; any positive value any positive value; any value

A

There are more possible samples that can be selected using theoretical sampling than using experimental sampling for any sample size greater than 1. True False

A

Two outcomes are said to be mutually exclusive when A) the probability of the two outcomes occurring together is equal to zero (p = 0) B) the probability of the occurrence of one outcome has no effect on the probability of the occurrence of the second outcome C) the probability of the two outcomes occurring together is greater than zero (p > 0) D) the probability of the two outcomes occurring together sums to one

A

While the expected value of the mean estimates the average outcome, the standard deviation of a probability distribution estimates the distance that all other outcomes deviate from the mean. True False

A

A normal distribution has a mean equal to 53. What is the standard deviation of this normal distribution if 2.5% of the proportion under the curve lies to the right of x = 66.72? (Round your answer to two decimal places) A) -7.00 B) 0.14 C) 7.00 D) 49.00

C

In a game, the probability of winning money is p = .16, the probability of losing money is p = .54, and the probability of breaking even is p = .30. What is the probability of winning or losing money in this game? .16 .54 .70 1.00

C

Suppose that a researcher selects a sample of participants from a population. If the shape of the distribution in this population is positively skewed, then what is the shape of the sampling distribution of sample means? A) approximately positively skewed B) approximately negatively skewed C) approximately normally distributed D) There is not enough information to answer this question, because the population mean and variance are not given.

C

Suppose you select a sample of three people from a population of four (A, B, C, D). Which of the following samples is possible using the experimental sampling strategy? persons A, C, and A persons A, D, and D persons B, C, and D persons B, A, and B

C

The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean? Researcher A: n = 25, u = 5, o = 7 Researcher B: n = 25, u= 32, o= 7 A) Researcher A B) Researcher B C) They both have the same standard error.

C

The normal distribution has all of the following characteristics, except A) the mean can be any number B) it is mathematically defined C) the total area under the curve is greater than 1.0 D) the mean, median, and mode are equal

C

What does it mean to say that the sample mean is an unbiased estimator of the population mean? A) The sample means will vary minimally from the population mean. B) The sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population. C) If we select a sample at random, then on average we can expect the sample mean to equal the population mean. D) all of the above

C

What values are distributed along the x-axis for a sampling distribution of the sample variance? A) scores B) sample means C) sample variances D) both B and C

C

Which of the following is not a step to locate a score in a normal distribution? Locate a z score associated with a given proportion in the unit normal table. Transform the z score into a raw score (x). Transform a raw score (x) into a z score.

C

20. A theoretical distribution that evenly distributes data around the mean, median, and mode is called the A) normal distribution B) bell-shaped distribution C) Gaussian distribution D) all of the above

D

63. The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making at most five errors. A) .29 B) .43 C) .57 D) .71

D

A researcher records the following data for the number of bids made on a sample of items sold at an auction. Based on the table, what was the probability that an item had 7 bids made on it? Number of Bids Frequencies 3 5 4 12 5 7 6 6 7 10 A) 5 B) 10 C) .10 D) .25

D

Increasing the number of observations or samples in a study will decrease the standard error (standard error of the mean). This is known as A) Bob (not the right answer) B) the law of diminishing returns C) the theoretical law of estimtates D) the law of large numbers

D

The sample variance is an unbiased estimator of the population variance when dividing SS by n when dividing SS by df when dividing SS by n - 1 both B and C

D

The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a A) standardized score B) x-score C) normalized deviation D) z score

D

When the probability of one outcome changes depending on the occurrence of a second outcome, these outcomes are referred to as mutually exclusive complementary independent conditional

D

Why doesn't the z-table tell you probabilities for negative z-scores?

because you must know the normal distribution is symmetrical

Name the four types of relationships between multiple outcomes

mutually exclusive outcome independent outcome complementary outcome conditional outcome

The proportion or fraction of times an outcome is likely to occur is referred to as probability a random event sample space luck

probability