Chapter 5 Statistics

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? Yes, because the z score for 5 bites is greater than 0. Yes, because the z score for 5 bites is less than 0. No, because the z score for 5 bites is greater than 0. No, because the z score for 5 bites is less than 0.

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

What is the z score for scores in the top and bottom 2.5%? +1.96 1.96 .0124 ±.675

+1.96

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 minutes per week? 1.0 -1.0 0 There is not enough information to answer this question.

-1.0

What is the z score for scores in the bottom 10%? 1.28 2.32 -2.32 -1.28

-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? .3413 .1587 .8413 The probability is not listed in the unit normal table.

.8413

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

0; 1

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)? 1.75 1.50 1.25 There is not enough information to answer this question.

1.75

What is the z score for scores in the top 2.5%? Selected Answer: 1.96 .0124 .0250

1.96

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 1/2 1/3 2/3 1.00

1/3

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

19.68 minutes.

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? 17.75 seconds 28.25 seconds faster than 16 seconds There is not enough information to answer this question.

28.25 seconds

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? 0.84 47.04 36.96 There is not enough information to answer this question.

47.04

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? 1.08 70.44 85.56 There is not enough information to answer this question.

85.56

A distribution of z scores are distributed in what type of unit of measurement? Binomial outcomes Probabilities Standard deviation units Depends on the shape of the distribution

Standard deviation units

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

The first area is bigger.

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

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

State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the right of the mean, or the area between z = ±1.00. The first area is bigger. The second area is bigger. The two areas are the same.

The second area is bigger.

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 2 symptoms per day is 0. Assuming the data are normally distributed, did she reach her goal? No, because the z score indicates 0 improvement. No, because the z score is not negative (indicating a reduction in symptoms). Yes; in fact, she actually reduced the mean number of symptoms to 0. Yes, because a z score of 0 is the average, or mean.

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

The following distribution most closely approximates a Refer to the Image. normal distribution positively skewed distribution negatively skewed distribution multimodal distribution

normal distribution

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

probability

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

z score

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 seconds or less? .1660 .3340 .6660 The probability is not listed in the unit normal table.

.1660

Which of the following is a possible value for the standard deviation of a normal distribution? -∞ 0 -2 .5

.5

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 .05 .50 200 400

.50

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 to 8 hours as moderate sleepers. What percentage of participants fell in this category? about 39% about 11% about 35% about 7%

about 35%

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

all of the above

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

approximate

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

both A and B

Which of the following is required to locate z scores with a given proportion? Find the z score associated with a given probability. Compute a z-transformation to find the raw score. both A and B none of the above

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 equal to the number of residents who support the new smoking ban equal to the total number (or population) of residents equal to more than just these 1,200 residents unknown

equal to the total number (or population) of residents

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 less than 0 greater than 0 exactly equal to 0 There is not enough information to answer this question.

exactly equal to 0

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

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. body tails most sensitive areas most uncertain areas

tails

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

that extreme scores are possible in a normal distribution

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

the sample space

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

the total area under the curve is greater than 1.0

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

there are an infinite number of possible normal distributions

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 category? .4834 .1753 .8413 .8247

.8247

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 minutes per week? 1.0 -1.0 .3413 .1587

-1.0

What is the z score for scores in the bottom 5%? 1.645 -1.645 .4801 The score is not listed in the table.

-1.645

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 9 birdcalls during this experimental session? .9987 .4987 .0013 The probability is not listed in the unit normal table.

.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 .86 .60 .43 86

.43

A researcher measures the number of tasks completed by participants during a 5-minute 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? .0446 .9554 .4554 The probability is not listed in the unit normal table.

.9554

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

Convert a proportion to a standard normal z score.

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? The first z distribution. The second distribution. None, the z score will be the same.

None, the z score will be the same.

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

Probability is most useful for describing fixed events.

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

The two areas are the same.

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.

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

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

all of the above

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

all of the above

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. normal distribution standard normal distribution standard normal transformation unit normal table

standard normal transformation