Statistics chapter 5

What is the z score for scores in the top 2.5%? a. 0.0124 b. 0.675 c. +1.96 d. 0.0250

c. +1.96

What is the z score for scores in the top and bottom 2.5%? a. 1.96 b. 0.0124 c. ±1.96 d. ±0.675

c. ±1.96

A researcher records the following response times to a visual stimulus: 23 ± 3.1 (M ± SD) seconds. Assuming these data are normally distributed, what is the probability that participants responded in 20 s or less? a. .6660 b. .3340 c. .1660 d. The probability is not listed in the unit normal table.

c. .1660

A researcher records the following body mass index (BMI) scores for a group of participants: 28.4 ± 1.6 (M ± SD). Participants who score between 25 and 30 on this scale are categorized as overweight. What percentage of participants fell in this overweight category? a. .4834 b. .8413 c. .8247 d. .1753

c. .8247

Which of the following is a possible value for the standard deviation of a normal distribution? a. -2 b. -∞ c. 0.5 d. 0

c. 0.5

A professor finds that the students scored a 76 ± 8 (M ± SD) on the final exam. On this exam, a score of 90 is an A. Assuming these data are normally distributed, what is the z score for 90 (the cutoff for an A)? a. 1.50 b. 1.25 c. 1.75 d. There is not enough information to answer this question.

c. 1.75

A professor records the following final exam scores: 78 ± 7 (M ± SD). Students scoring in the top 14% get an A. What is the cutoff score for the top 14% in this example? a. There is not enough information to answer this question. b. 1.08 c. 85.56 d. 70.44

c. 85.56

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

b. -1.645

What is the z score for scores in the bottom 10%? a. -1.28 b. 1.28 c. -2.32 d. 2.32

a. -1.28

A counselor records the number of disagreements (per session) among couples during group counseling sessions. If the number of disagreements is distributed normally as 4.4 ± 0.4 (M ± SD) disagreements, then what proportion of couples disagree at least 4 times during each counseling session? a. .8413 b. .1587 c. The probability is not listed in the unit normal table. d. .3413

a. .8413

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

a. 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 ______. a. 1/3 b. 1/2 c. 2/3 d. 1.00

a. 1/3

Two normal distributions are observed. The first distribution has a mean of 12 and a standard deviation of 2. The second distribution has a mean of 0 and a standard deviation of 2. For which distribution will the z score for the mean be larger? a. None, the z score will be the same. b. the second distribution c. the first z distribution

a. None, the z score will be the same.

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.

a. The second area is bigger. b. The first area is bigger. c. The two areas are the same.

a. The second area is bigger.

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

a. transform a raw score (x) into a z score

A researcher determines that students are active about 60 ± 12 (M ± SD) minutes per day. Assuming these data are normally distributed, what is the z score for students being active 48 min per week? a. There is not enough information to answer this question. b. -1.0 c. 1.0 d. 0

b. -1.0

A researcher determines that students study an average of 80 ± 20 (M ± SD) minutes per week. Assuming these data are normally distributed, what is the z score for students studying 60 min per week? a. 0.1587 b. -1.0 c. 0.3413 d. 1.0

b. -1.0

A researcher records the following number of birdcalls made during an experimental session with robins: 7.2 ± 0.6 (M ± SD). Assuming these data are normally distributed, what is the probability that robins made more than nine birdcalls during this experimental session? a. .9987 b. .0013 c. .4987 d. The probability is not listed in the unit normal table.

b. .0013

A researcher has participants 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. .86 b. .43 c. .60 d. 86

b. .43

A researcher measures the number of tasks completed by participants during a 5-min multitasking session. If the number of tasks completed is distributed normally as 6.3 ± 1.0 (M ± SD) tasks, then what is the probability that participants completed less than 8 tasks? a. .4554 b. .9554 c. The probability is not listed in the unit normal table. d. .0446

b. .9554

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

b. 0.50

A researcher records the following assessment data: 42 ± 6 (M ± SD). The researcher only wants to sample participants scoring in the top 20% of this assessment. What is the cutoff score for the top 20% in this example? a. There is not enough information to answer this question. b. 47.04 c. 0.84 d. 36.96

b. 47.04

Most behavior is believed to ______ a normal distribution. a. be exactly equal to b. approximate c. not resemble at all

b. approximate

Which of the following is not a step to locate a proportion in a normal distribution? a. locate the corresponding proportion for the z score in the unit normal table b. convert a proportion to a standard normal z score c. transform a raw score (x) into a z score

b. convert a proportion to a standard normal z score

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. exactly equal to 0 c. there is not enough information to answer this question d. greater than 0

b. exactly equal to 0

The following distribution most closely approximates a ______. a. positively skewed distribution b. normal distribution c. multimodal distribution d. negatively skewed distribution

b. normal distribution

The ______ converts any normal distribution with any mean and any variance to a standard normal distribution with a mean of 0 and variance of 1. a. normal distribution b. standard normal transformation c. standard normal distribution d. unit normal table

b. standard normal transformation

What is the implication for the tails of a normal distribution being asymptotic? a. that this characteristic has no practical implication b. that extreme scores are possible in the tails of a normal distribution c. that there are an infinite number of possible normal distributions d. that scores above the mean are distributed the same as scores below the mean

b. that extreme scores are possible in the tails of a normal distribution

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

b. the sample space

The mean can take on any value and the standard deviation can take on any positive value. Therefore, ______. a. extreme scores are possible in a normal distribution b. there are an infinite number of possible normal distributions c. this characteristic has no practical implication d. scores above the mean are distributed the same as scores below the mean

b. there are an infinite number of possible normal distributions

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.

A therapist has a goal to reduce the mean number of patient symptoms expressed for a particular disorder to two symptoms per day. Following therapy, she determines that the z score for two symptoms per day is 0. Assuming these data are normally distributed, did she reach her goal? a. No, because the z score indicates 0 improvement. b. Yes; in fact, she actually reduced the mean number of symptoms to 0. c. Yes, because a z score of 0 is the average, or mean. d. No, because the z score is not negative (indicating a reduction in symptoms).

c. Yes, because a z score of 0 is the average, or mean.

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 these

c. both A and B

Which of the following is required to locate z scores with a given proportion? a. find the z score associated with a given probability b. compute a z transformation to find the raw score c. both A and B d. none of these

c. both A and B

A researcher visits a population of 1,200 local residents to determine the proportion of local residents who support a new smoking ban. In this case, the sample space is ______. a. unknown b. equal to the number of local residents who smoke c. equal to the population of 1,200 local residents d. equal to the number of residents who support the new smoking ban

c. equal to the population of 1,200 local residents

The normal distribution is symmetrical, which means that ______. a. there are an infinite number of possible normal distributions b. this characteristic has no practical implication c. scores above the mean are distributed the same as scores below the mean d. extreme scores are possible in a normal distribution

c. 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. a. most sensitive areas b. body c. tails d. most uncertain areas

c. tails

The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a ______. a. x score b. standardized score c. z score d. normalized deviation

c. z score

A researcher records the following times (in seconds) that it took a group of students to complete an exam: 18 ± 2 min (M ± SD). How long did it take 80% of students to complete the exam? a. 16.32 min b. less than 18 min c. less than 16 min d. 19.68 min

d. 19.68 min

A researcher records the following times (in seconds) that it took a group of mice to complete a maze: 23 ± 4.1 (M ± SD). The top 10% of mice finishing with the fastest times will be placed in a "maze bright" group. What is the cutoff time to be placed in this group? a. 17.75 s b. There is not enough information to answer this question. c. faster than 16 s d. 28.25 s

d. 28.25 s

A parent decides to reward her child if he eats an average of at least five bites of his vegetables at dinner during the first week. She finds that her child ate 4 ± 0.8 (M ± SD) bites per meal for the first week. Assuming these data are normally distributed, should this parent reward her child? a. Yes, because the z score for 5 bites is greater than 0. b. No, because the z score for 5 bites is less than 0. c. Yes, because the z score for 5 bites is less than 0. d. No, because the z score for 5 bites is greater than 0.

d. No, because the z score for 5 bites is greater than 0.

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

d. Probability is most useful for describing fixed events.

Which of the following describes the largest proportion in a z distribution? a. The proportion of area less than z = 0. b. The proportion of area above the mean. c. The proportion of area greater than z = 1.0. d. The proportion of area between z = +1 and z = -1.

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

A researcher records the following time spent sleeping per night (in hours) in a group of participants: 5.8 ± 1.8 (M ± SD). The researcher decides to categorize participants who sleep between 6 and 8 hr as moderate sleepers. What percentage of participants fell in this category? a. about 11% b. about 7% c. about 39% d. about 35%

d. about 35%

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 these

d. all of these

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 these

d. all of these

In a normal distribution, 50% of all data ______. a. fall above the mean b. fall below the median c. fall above and below the mode d. all of these

d. all of these

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

d. probability

A distribution of z scores are distributed in what type of unit of measurement? a. probabilities b. binomial outcomes c. depends on the shape of the distribution d. standard deviation units

d. standard deviation units

The normal distribution has all of the following characteristics, except that ______. a. the mean, median, and mode are equal b. it is symmetrical c. its distribution is theoretical d. the total area under the curve is greater than 1.0

d. the total area under the curve is greater than 1.0