Psych 311 - Exam 2 Study Guide

Suppose that the probability that any child of alcoholic parents becomes alcoholic is p = .16. Assuming independent outcomes, the probability that two children of alcoholic parents will be alcoholic equals

.03

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: 3, 4, 5, 6, 7 Frequencies: 5, 12, 7, 6, 10

.25

The probability that someone in the human population has blood type AB is about p = .08; the probability that someone has blood type O is about p = .25. Knowing that each individual can have one and only one blood type, what is the probability that a person has an AB or O blood type?

.33

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?

.70

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.

21.7 students

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.

32

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 B, C, and D

Regardless of the shape of the distribution in the population, the sampling distribution of sample variances approximates a

positively skewed distribution

The proportion or fraction of times an outcome is likely to occur is referred to as

probability

The DISTRIBUTION of PROBABILITIES for each outcome of a random variable that sums to 1.00 is called a

probability distribution

The normal distribution is symmetrical, which means that

scores above the mean are distributed the same as scores below the mean

Scores far from the mean are located in the ________ of a normal distribution.

tails

What is the implication for the tails of a normal distribution being asymptotic?

that extreme scores are possible in a normal distribution

Each of the following statements are true, except that

the larger the sample size, the larger the standard error

Increasing the number of observations or samples in a study will decrease the standard error (standard error of the mean). This is known as

the law of large numbers

Two outcomes are said to be mutually exclusive when

the probability of the two outcomes occurring together is equal to zero (p = 0)

The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a

z score

What does it mean to say that the sample mean is an unbiased estimator of the population mean?

If we select a sample at random, then on average we can expect the sample mean to equal the population mean.

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 sampling distribution

Define the central limit theorem.

a statistical theory that states that 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

Which rule states that when two outcomes are mutually exclusive, the probability that either one of these outcomes will occur is the sum of their individual probabilities?

additive rule

Most behavior is believed to ________ a normal distribution.

approximate

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?

approximately normally distributed

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

b

The mean of the sampling distribution of sample means is

equal to the population mean

The mean of a probability distribution is called the

expected value of the mean; mathematical expectation

The following distribution most closely approximates a

a

What is the z score for scores in the bottom 10%?

-1.28

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?

1,000,000

If the standard deviation of a probability distribution is 9, then the variance is

81

Which proportion is largest in a z distribution?

The proportion of area between z = +1 and z = -1.

p(U / P) is equal to

p(P ∩ U)/ p(P)

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 = (2-8)/2

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?

.50

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.

.71

The standard normal distribution is normally distributed with a mean of ____ and a variance of ____.

0; 1

A news poll showed that voters had no preference for either of three candidates. In this example, the probability of a vote for, say, Candidate A equals

1/3

A gambler rolls a 3 with one roll of a single fair die. Given that the die was six-sided, what was the probability of rolling a 3 with one roll?

1/6

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?

15

The following are six random outcomes for a sample space: -1, -3, -3, -2, -5, and -6. What is the probability of selecting a -3 in this example?

2/6

How many possible samples of size 2 can be selected from a population of 5 using theoretical sampling?

25

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

36 and 40

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?

40

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.

48 students

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)

7.00

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

9 and 10

How is the standard error of the mean typically reported in a graph?

using error bars

The SAMPLE VARIANCE is an unbiased estimator of the POPULATION VARIANCE when...

- when dividing sum of squares (SS) by df - when dividing SS by n - 1

What is the z score for scores in the bottom 5%?

-1.645

In a normal distribution, 50% of all data:

- fall above the mean - fall below the median - fall above and below the mode

A theoretical DISTRIBUTION that evenly distributes data around the mean, median, and mode is called the

- normal distribution - bell-shaped distribution - Gaussian distribution

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

C) Transform a raw score (x) into a z score.

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) the total area under the curve is greater than 1.0

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) the time it takes to complete a driving test

TRUE OR FALSE: A binomial probability distribution is constructed for random variables that have at least two possible outcomes.

False

TRUE OR FALSE: 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.

False

TRUE OR FALSE: In a normal distribution a score of 8 will ALWAYS be more probable than a score of 0.

False

TRUE OR FALSE: The central limit theorem states that the sample mean will equal the population mean on average.

False

TRUE OR FALSE: The probability of an outcome is particularly useful for predicting the likelihood of fixed events.

False

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

They both have the same standard error.

TRUE OR FALSE: 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

TRUE OR FALSE: For a set of data with 25±2.5, at least 95% of scores fall between 20 and 30.

True

TRUE OR FALSE: Probability distributions display the probability of each possible outcome for a given random variable.

True

TRUE OR FALSE: Probability ranges between 0 and 1 and is never negative.

True

TRUE OR FALSE: The average sample variance equals the population variance when dividing SS by df.

True

TRUE OR FALSE: The expected value of a random variable is the mean of a probability distribution.

True

TRUE OR FALSE: 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

TRUE OR FALSE: The sample mean is an unbiased estimator of the population mean.

True

TRUE OR FALSE: The sample space is equal to the total number of random outcomes possible for a random variable.

True

TRUE OR FALSE: The sampling distribution of the mean has minimum variance.

True

TRUE OR FALSE: 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

TRUE OR FALSE: The standard error of the mean is the standard deviation in a sampling distribution of sample means.

True

TRUE OR FALSE: There are 25 possible samples of size 2 that can be selected from a population of 5 people using theoretical sampling.

True

TRUE OR FALSE: There are more possible samples that can be selected using theoretical sampling than using experimental sampling for any sample size greater than 1.

True

TRUE OR FALSE: 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

TRUE OR FALSE: binomial probability distribution is the distribution of random outcomes for a bivariate or dichotomous random variable.

True

As sample size INCREASES, the standard error of the mean

decreases

Bayes' theorem is often applied to a variety of ________ probability situations, including those related to statistical inference.

conditional

When the probability of one outcome changes depending on the occurrence of a second outcome, these outcomes are referred to as

d

A researcher selects a sample of 16 participants from a population with a variance of 4. What is the standard error of the mean?

less than 1

Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities?

multiplicative rule

What values are distributed along the x-axis for a sampling distribution of the sample mean?

sample means

What values are distributed along the x-axis for a sampling distribution of the sample variance?

sample variances

For the experimental sampling strategy..

sampling is without replacement

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