Stats: Exam 2

T or F: Complementary outcomes are exhaustive of all possible outcomes.

True

What is the z-score for the scores in the bottom 5%? a. 1.645 b. -1.645 c. 0.4801 d. the score is not listed in the table

b. -1.645

A therapist goes through her records and finds that 200 of her 400 patients showed significant improvement is mental health over the past year. Hence, the probability of her patients showing significant improvement in mental health is: a. 0.05 b. 0.50 c. 200 d. 400

b. 0.50

As a sample size increases, the standard error of the mean: a. increases b. decreases c. can increase or decrease d. does not change

b. decreases

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. tails

A researcher has participant choose between three advertisements. She finds that 54 prefer ad A, 86 prefer ad B, and 60 prefer ad C. The probability or proportion of participants preferring ad B is: a. 0.86 b. 0.60 c. 0.43 d. 86

c. 0.43

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. all of the above

The sample variance is an unbiased estimator of the population variance: a. when dividing SS by n b. when dividing SS by df c. when dividing SS by n-1 d. both B and C

d. both B and C

T or F: A sampling distribution is a distribution of scores in a population.

false

T or F: Researchers typically sample with replacement, although the development of statistical theory was based on the use of sampling without replacement.

false

T or F: The central limit theorem states that the sample mean will equal the population mean on average.

false

The probability of a student attending every college class is p=0.26. The probability of a student attending every college class and earning an A is p=0.22. Hence, the probability of a student earning an A, given that he or she attends every college class is: a. p=0.06 b. p=0.48 c. p=0.85 d. there is not enough information to answer this question

p=0.85

T or F: A binomial probability distribution is the distribution of random outcomes for a bivariate or dichotomous random variable.

true

T or F: Conditional outcomes refer to those where the probability of one outcome is independent of the probability of the occurrence of the second outcome.

False

T or F: In a normal distribution with 2.2+/-4.1 (M+/-SD), a researcher can appropriately conclude that most scores occur above the mean.

False

T or F: The multiplicative rule is used to define mutually exclusive outcomes.

False

T or F: Mathematical expectation can be used to estimate the expected value of variance and standard deviation.

True

T or F: The following probability distribution for outcomes 0, 1, 2, and 3, respectively, is possible: 18/30, 3/30, 4/30, and 5/30.

True

T or F: 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

T or F: Without knowing a thing about the population variance, we can expect a randomly selected sample variance (sample variance=SS/df) to equal the population variance on average.

True

T or F: The binomial probability distribution is distributed with u=np and o=(square root)npq.

True

A researcher records the following response times to a visual stimulus: 23 +/- 3.1 (M+/-SD). Assuming these data are normally distributed, what is the probability that participants responded in 20 seconds or less? a) .1660 b) .334 c) .660 d) The probability is not listed in the unit normal table.

a) .1660

The distribution of probabilities for each outcome of a random variable that sums to 1.00 is called a: a. random variable b. probability distribution c. condition probability d. sample space

b. probability distribution

The total number of possible outcomes for a random variable is referred to as: a) probability b) a random event c) the sample space d) the sum

c) the sample space

A researcher records the following data for the number of bids made on a sample of items at an auction. Based on the table, what is the probability that an item had 7 bids on it? # bids: 3, 4, 5, 6, 7 Frequencies: 5, 12, 7, 6, 10 a) 5 b) 10 c) .10 d) .25

c) .10

A researcher records the # of job openings amongst small businesses. She finds the probability that a small business has 0 job openings is p=.22, 1 job opening is p=.45, 2 job openings is p=.08, 3 job openings is p=.25. What is the probability that a small business has at least 2 job openings? a) .08 b) .25 c) .33 d) .67

c) .33

If the standard deviation of a probability distribution is 9, then the variance is: a. 3 b. 9 c. 81 d. unknown

c. 81

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. both A and B

Which of the following is required to locate proportions of area under the normal curve? a. compute a z-transformation. b. find the probability of a z-score in the unit normal table. c. both A and B d. none of the above

c. both A and B

A researcher finds that the average preschool-aged child drinks two cups of milk per day. Assuming these data are normally distributed, the z-score for the average cups per day in this example is a. less than 0 b. greater than 0 c. exactly equal to 0 d. there is not enough information to answer this question.

c. exactly equal to 0

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

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? a. persons A, C, and A b. persons A, D, and D c. persons B, C, and D d. persons B, A, and B

c. persons B, C, and D

The normal distribution has all of the following characteristics, except that: a. it is symmetrical b. its distribution is theoretical 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

State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the left of z = 0.80, or the area to the right of z = -0.80. a. the first area is bigger. b. the second area is bigger. c. the two areas are the same.

c. the two areas are the same.

T or F: The expected value of a random variable is the mean of a probability distribution.

true

T or F: The mean of a binomial distribution is the product of the number of trials (n) times the probability of the outcome of interest on an individual trial (p).

true

T or F: The sample mean is an unbiased estimator of the population mean.

true

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. a sampling distribution

A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5. What is the probability of selecting a sample mean equal to at least 12? a. less than 1% b. greater than 50% c. about the same as selecting a sample mean that is at least equal to the population mean d. equal to the probability of selecting a sample mean that is smaller than 8

d. equal to the probability of selecting a sample mean that is smaller than 8

T or F: A sample mean is not always equal to a population mean-- it can vary from sample to sample.

true

T or F: Probability ranges between 0 and 1 and is never negative.

true

T or F: As sample size decreases, the standard of error also decreases.

False

T or F: The mean of a sampling distribution of sample means is an unbiased estimator of the population mean.

True

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 is p=.25. Knowing that each individual can have only one blood type, what is the probability that each individual has AB or O blood type? a) .33 b) .02 c) 1.00 d) this state of affairs is not possible.

a) .33

Which rule states that when 2 outcomes are mutually exclusive, the probability that either of these outcomes will occur is the sum of their individual probabilities? a) additive rule b) multiplication rule c) both a and b d) none of the above

a) additive rule

Suppose that a researcher selects a sample of participants from a population. If the shape of the distribution in this population is negatively skewed, then what is the shape of the sampling distribution of sample variance? a) approximately positively skewed b) approximately negatively skewed c) approximately normally distributed d) There is not enough information to answer this question

a) approximately positively skewed

A researcher records the number of buckets of popcorn purchased by patrons during 1 night at the movies. She finds that the probability that a patron purchased 0 buckets is p=.27, 1 bucket is p=.51, 2 buckets is p=.17, 3 buckets is p=.05. How many buckets of popcorn can we expect a patron to purchase per night at the movies? a) exactly 1 bucket of popcorn per night b) more than 1 bucket of popcorn per night c) less than 1 bucket of popcorn per night d) none of the above

a) exactly 1 bucket of popcorn per night

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

a) probability

2 outcomes are said to be mutually exclusive when: a) the probability of the 2 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 2 outcomes occurring together is greater than zero (p>0) d) the probability of the 2 outcomes occurring together sums to one

a) the probability of the 2 outcomes occurring together is equal to zero (p=0)

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

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

a. 0; 1

A distribution of probabilities for random outcomes of a bivariate or dichotomous random variable is called a: a. binomial probability distribution b. distribution of expected values c. random variable distribution d. mathematical expecation

a. binomial probability distribution

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

a. probability

The normal distribution is symmetrical, which means that: a. scores about 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 implications

a. scores about the mean are distributed the same as scores below the mean

State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the left of z = 1.00, or the area to the left of z = -1.00. a. the first area is bigger. b. the second area is bigger. c. the two areas are the same.

a. the first area is bigger

What is the central limit theorem? a. it explains that sample means will vary minimally from the population mean b. it explains that a sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population c. it explains that 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

b. it explains that a sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population

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. that extreme scores are possible in a normal distribution

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. the larger the sample size, the larger the standard error

The probability that a parent rewards a child with a dessert for eating a healthy meal is .07. Assuming independent outcomes, the probability that two parents reward their child's healthy eating equals: a) .07 b) .14 c) .05 d) .005

d) .005

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=.1, earns a F is p=.08. If the failing grade is D or less, then what is the probability that a student fails the class? a) .08 b) .10 c) .20 d) .18

d) .18

Which of the following is NOT a characteristic of probability? a) Probability varies between 0 and 1. b) Probability can never be negative. c) Probability can be stated as a fraction or decimal. d) Probability is most useful for describing fixed events.

d) Probability is most useful for describing fixed events.

By definition, the probability of an outcome or event is: a) the proportion of times an outcome is likely to occur b) the fraction of times an outcome is likely to occur c) particularly useful for predicting the likelihood of random events d) all of the above

d) all of the above

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

d) conditional