Chapter 6 Test Questions

When two normal z-distributions are plotted on the same graph, what can we say about the relative frequency of each z-score? a. It will always be the same b. It will always be different C. It depends on the raw score mean d. It depends on the raw score standard deviation

A

A theoretically perfect normal curve, which serves as a model of the perfect normal z-distribution is called the a. sampling distribution of means b. standard, normalized z-distribution c. standard normal curve d. standard mean score distribution

C

In a z-distribution, the standard deviation will always be a. greater than 1 b. less than 1 c. equal to 1 d. equal to 0

C

The mean of a z-score distribution is always ______, and the standard deviation is always ____________. a. 0;10 B. 1;0 C. 100;20 D. 0;1

D

Using the appropriate values from the z-table in the textbook appendix, find the z-score for which the area beyond z in the tail is .2546. a. .66 b. .2454 c. -.66 d. -.2454

A

When the standard deviation of a raw score distribution is large, the corresponding z-score distribution will be a. relatively spread out b. relatively narrow c. positively skewed d. negatively skewed

A

For a distribution with x̄=50 and Sx=5, find the z-scores for each of the following raw scores: 50;65;45;42 a. 0;-3;1;1.6 b. 0; 6.71; -2.24; -3.58 c. 0; 3; -1; -1.6 d. 0; -6.71; 2.24; 3.58

C

an evaluation of where a score is located in relation to the other scores in the distribution reflects its a. absolute value b. relative standing c. standard deviation d. frequency

b

Sampling distributions of means are always a. approximately normally distributed b. positively skewed c. negatively skewed d. more variable than the population from which the samples were drawn

a

Your sense of direction puts you at the 39th percentile, relative to a raw score distribution with a mean of 3.5 and a standard deviation of 1. What is your z-score? a. -.28 b. +.28 c. +1.23 D. -1.23

A

The relative frequency(ies) obtained from the standard normal curve is (are) the __________ of the raw scores in our data, if the data formed a perfect normal distribution. a. z-scores b. expected relative frequency c. expected simple frequency d. model

B

According to the central limit theorem, the sampling distribution of means always approximates a ________ distribution. a. normal b. positively skewed c. negatively skewed d. bimodal

a

Alicia scored a 70 on her psychology quiz, but the class as a whole averaged a 40. If the standard deviation was 10 what was alicia's z-score? a. -3 b. +3 c. -.3 d +.3

B

As the N of the samples used in a sampling distribution _______, the sampling distribution becomes ______. a. decreases; more like a perfect normal curve b. increases; more like a perfect normal curve c. decreases; less spread out d. increases; more spread out

B

For the following set of scores, what is the z-score for a raw score of 23? 22,23,19,25,26,22,19,25,22,20,21,23,23,24,18,20, 22,24,21,21,20,24,22,21,23 a. 1.25 b. .50 c. .34 d. .68

B

Given a normal distribution, as z-scores' absolute values increase, those z-scores and the raw scores that correspond to them occur a. more frequently b. less frequently c. more frequently at first and then less frequently d. less frequently at first and then more frequently

B

Given any z-score, it is safe to say that the absolute value is a good indicator of ____________ and the sign (+ or -) is a good indicator of ___________. A. direction; distance b. distance; direction c. frequency; amount d. amount; frequency

B

In sampling distributions, all the samples contain sets of raw scores a. with the same variance b. from the same population c. with the same mean d. that are representative of the population mean

B

On a recent paper, Maria's score, transformed to a z-score, was a +1. If the cutoff mark is the upper 10% of the class for As, the upper 10% to 20% for B's, the upper 20% to 30% for C's, and the upper 30% to 40% for D's (below 60% being a failure), what grade did maria receive on the quiz? A. A B. B C. C D. F

B

One way to measure the ability to find one's way in an environment is to ask people to rate themselves on a sense of direction scale. The scale ranges from 1 (poor) to 7 (good). In a sample of college students, including yourself, the mean rating of sense of direction is 3, with a standard deviation of 1. If you gave yourself a rating of 2, what is your z-score? A. .57 B. -1.0 C. +1.5 D. 2.0

B

The mean of the sampling distribution always equals a. the mean of the sample, when the sample N is large b. the mean of the underlying raw score population c. 0 d 1

B

The sample mean for a recent introductory psychology test was 78, and the sample variance was 9. If a student received a score of 82, what was this student's z-score? a. .44 b. 1.33 c. -1.33 d. -.44

B

To evaluate a person for possible brain damage, a neuropsychologist gives the person a visual memory test and a reading test. To compare the person's performance across these two tests, what should the neuropsychologist do? A. Graph the raw score distribution for each test on the same graph B. Calculate a z-score for each test C. calculate z-scores for the sample means D. Find the simple frequency of the person's raw score for each test

B

Using the appropriate values from the z-table in the textbook appendix, find the area above (beyond) z=+.89 a. .3133 b. .1867 c. -.3133 d. -.1867

B

What raw score is at the 16th percentile (15.87 to be exact) when the mean of the distribution is 50 and the standard deviation is 4? a. 54 b. 46 c. 34 d. There is insufficient information to determine an answer

B

What were the sample means that marked the middle 68% in the state if the population mean was 500 and the standard deviation (standard error) for the sampling distribution was 200? a. 350 and 650 b. 300 and 700 c. 400 and 600 d. 450 and 550

B

Z-scores can be calculated from a. any data b. interval or ratio scores c. nominal or ordinal scores d. the range

B

Z-scores communicate a score's a. absolute magnitude b. relative location in a distribution c. distance from the population mean d. variability

B

If a class's scores are normally distributed, with a mean of 70 and a standard deviation of 10, what are the upper and lower limits of the middle 68% of the class? A. 50 and 90 B. 40 and 100 C. 60 and 80 D. 32 and 68

C

If raw scores ranging from 1-50 represented all the corresponding negative z-scores on the distribution, and raw scores ranging from 50 to 100 represented all the corresponding positive z-scores, what would be the total relative frequency of 50 to 100? A. 1.00 B. .75 C. .5 D. .25

C

If there were 500 students in Jamal's class, approximately how many actual students scored higher than Jamal on the quiz if Jamal had a z-score of -2? a. 250 b. 340 c. 420 d. 490

C

Pat's last statistics test score was 72. If the instructor tells Pat that the grade distribution was approximately normal, the class mean was 67, and the standard deviation was 3, which of the following is correct? a. A score of 72 is never good. B. Pat should be worried about this score, because many other students did better c. Pat should be fairly happy about this score, because many students did not do as well d. Pay should be ecstatic, because this is obviously one of the highest grades in the class

C

The average score on the statistics quiz was a 70, and there was a standard deviation of 10 points. If Enrique had a z-score of -1.0, his raw score would be _______ and his percentile rank would be _______. a. 40; 2% b. 50; 16% c. 60; 16% d. 60; 34%

C

The distribution of z-scores is always a. positively skewed b. negatively skewed c. the same as the distribution of raw scores d. more spread out than the distribution of raw scores

C

The mean of the sampling distribution of means is always a. greater than the population mean b. less than the population mean c. equal to the population mean d. the population mean divided by the square root of N

C

The sample mean for a recent introductory psychology test was 78, and the sample variance was 9. If a student's z-score=-2.0, what was this student's raw test score? a. 84 b. 60 c. 72 d. 96

C

We can use the standard normal curve as our model for a. perfectly normal distributions only b perfectly normal distributions only, when transformed to z-scores c. any approximately normal distribution, when transformed to z-scores. d. any approximately normal distribution when transformed to percentiles

C

Your sense of direction puts you at the 79th percentile, relative to a raw score distribution with a mean of 3.5 and a standard deviation of 1. What is your z-score? a. +.13 B. +.5 C. +.81 D. -.81

C

A sampling distribution of means for samples of students taking the SAT exam has a population mean of 500 and a standard error of 200. What proportion of sample means would fall between the population mean and a sample mean of 800? a. .50000 b. .3413 c. .1915 d. .4332

D

A z-score of zero always means that a. the raw score does not exist b. the raw score exists but is negligible c. the raw score almost never occurs d. the raw score is equal to the mean

D

Chris wants to calculate a z-score for his own height. The average height in the class is 66 inches, and Chris's height in 62 inches. Chris calculated his z-score to be +1.5. What's wrong with his calculation? A. the z-score is an inappropriate calculation here b. The z-score should be a higher number c. He didn't have the standard deviation d. The z-score should be a negative number

D

If only the upper 30% of a normally distributed class passed a quiz for which the mean was 70 and the standard deviation was 10, what was the lowest score a student could have received and still have passed? a. 80 b. 64.8 c. 70 d. 75.2

D

If your sense of direction, relative to a sample of college students, gave you a z-score of +1.5 what is your percentile? a. 6th b. 7th c. 43rd d. 93rd

D

The proportion of the total area under a normal curve between two z-scores corresponds to the __________ of that range of scores. a. numeric magnitude b. variability c. frequency d. relative frequency

D

Which of the following is NOT one of the things the relative frequency of z-scores allows us to calculate for corresponding raw scores? A. Expected relative frequency B. Expected simple frequency C. Percentile rank D. Values in terms of goodness or badness

D

A sampling distribution is an approximately normal distribution a. regardless of the shape of the raw score distribution b. only when the shape of the raw score distribution is approximately normal c. only when the raw score population mean is equal to the sample mean d. regardless of the distribution of the sample means

a

For a distribution with x̄=50 and Sx=5, find the raw scores for the following z-scores: -1.2;-.5;1.7;2.6 a. 44.00; 47.50; 58.50; 63.00 b. 20.00;37.50;92.50;115.00 c. 47.32; 48.88; 53.80; 55.81 d. -20.00;-37.50;92.50;115.00

a

For each other the following z-scores, what is the area beyond the z-score in the tail? .63, -1.65, 1.94, -2.27, 2.8 a. .2643; .0495; .0262; .0116; .0026 b. .2643; -.0495; .0262; -.0116; .0026 c. .2357; .4505; .4738; .4884; .4974 d. .2357; -.4505; .4738; -.4884; .4974

a

For the following set of scores, what is the percentile for a score of 24? 23,22,19,25,26,22,19,25,22,20,21,23,23,24,18,20, 22,24,21,21,20,24,22,21,23 a. 84th percentile b. 34th percentile c. 16th percentile d. 50th percentile

a

How accurately the standard normal curve model predicts the actual relative frequency of raw scores depends on three aspects of the data? a. The raw scores form and approximately normal distribution; there is a large sample N; and the raw scores are theoretically continuous scores measured on an interval or ration scale b. 50% of the raw scores are above and below the median; there is a large sample N; and the raw scores are measured on an ordinal, interval or ratio scale. C. 50% of the raw scores are above and below the median; tehre is a moderately large sample N; the raw scores are theoretically continuous scores measured on an interval or ration scale D. The raw scores form an approximately normal distribution; there is a moderately large sample N; and the raw scores are measured on an ordinal, interval or ratio scale

a

If a school's z-score for its sample mean was +3, its percentile rank in the state was a. 99.87% b. 90.87% c. 85.87% d. 95.87%

a

Only the upper 30% of a normally distributed class passed a quiz for which the mean was 70 and the standard deviation was 10. In this class, 76.7 and 78.4 are the boundary limits for students who scored between what percentiles? a. 75th and 80th b. 80th and 85th c. 77th and 80th d. 67th and 80th

a

The z-score transformation is a useful statistical tool because it enables statisticians to a. compare and interpret scores from virtually any distribution b. determine which scores are the "best" scores c. transform data by multiplying by a constant d. revise the shape of distributions to be more useful

a

Bahatamy academy has an outrageously intelligent student body. In a recent evaluation of all the high schools in the state, Bahatamy Academy received a z-score of +3 for its corresponding sample mean of SAT scores. With a population mean of 500 and a standard deviation (standard error) of 200 for the sampling distribution, what was Bahatamy's sample mean? a. 560 b. 1560 c. 1100 d. 900

c

For each of the following z-scores, what is the area between the mean and each z-score? .4; 1.01; -1.48; -1.89; 2.53 a. .3446; 0.1562; .0694; .0294; .0057 b. .1554; .3438; -.4306; -.4706; .4943 c. .1554; .3438; .4306; .4706; .4943 d. .3446; .1562; -.0694; -.0294; .0057

c

Jason's z-score in the 10-K run was -3. If the raw score standard deviation was 5, and the mean running time for the competitors was 55 minute, what was Jason's raw score running time? a. 60 min b. 50 min c. 40 min d. 30 min

c

The sample mean for a recent introductory psychology test was 78 and the sample variance was 9. Approximately what proportion of the scores was about 81? a. .50 b. .68 c. .16 d. .34

c

The standard deviation of the sampling distribution of means is called the a. percent error of the mean b. likely error of the mean c. standard error of the mean d. special error of the mean

c

The absolute value is the number is the a. the measure of how much the number is worth b. size of a number only when it is a positive number c. size of a number only when it is a negative number d. numeric magnitude of the number, regardless of whether it is positive of negative

d

Which of the following statements accurately describes the sampling distribution of means? a. The distribution of several sample means when an infinite number of samples of the same size N are randomly selected from one raw score population b. The distribution of all possible sample means when a given finite number of samples of the same size N are randomly selected from one raw score population c. The distribution of all possible sample means when an infinite number of samples of variously sized Ns are randomly selected from several raw score populations d. The distribution of all possible sample means when an infinite number of samples of the same size N are randomly selected from one raw score population

d