**INSTANT DOWNLOAD COMPLETE TEST BANK WITH ANSWERS**** ****Understanding Statistics In the Behavioral Sciences 9th Edition by Robert R. Pagano – Test Bank**** ****Sample Questions** **Chapter 5—The Normal Curve and Standard Scores** **MULTIPLE CHOICE** **Exhibit 5-1**A stockbroker has kept a daily record of the value of a particular stock over the years and finds that prices of the stock form a normal distribution with a mean of $8.52 with a standard deviation of $2.38.

- Refer to Exhibit 5-1. The percentile rank of a price of $13.87 is ____.

a. | 48.78% |

b. | 1.22% |

c. | 98.78% |

d. | 51.22% |

ANS: C PTS: 1

- Refer to Exhibit 5-1. What percentage of the distribution lies between $5 and $11?

a. | 21.48% |

b. | 78.41% |

c. | 49.41% |

d. | 57.98% |

ANS: B PTS: 1

- Refer to Exhibit 5-1. What percentage of the distribution lies below $7.42?

a. | 17.72% |

b. | 32.28% |

c. | 82.28% |

d. | 31.92% |

ANS: B PTS: 1

- Refer to Exhibit 5-1. The stock price beyond which 0.05 of the distribution falls is ____.

a. | $ 4.60 |

b. | $12.47 |

c. | $ 4.57 |

d. | $12.44 |

ANS: D PTS: 1

- Refer to Exhibit 5-1. The percentage of scores that lie between $9.00 and $10.00 is ____.

a. | 15.31% |

b. | 31.17% |

c. | 23.24% |

d. | 7.93% |

ANS: A PTS: 1 **Exhibit 5-2**A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 with a standard deviation of 90. The scores are normally distributed.

- Refer to Exhibit 5-2. The percentile rank of a score of 667 is ____.

a. | 3.14% |

b. | 96.78% |

c. | 3.22% |

d. | 96.86% |

ANS: D PTS: 1

- Refer to Exhibit 5-2. The proportion of scores that lie above 650 is ____.

a. | 0.4535 |

b. | 0.9535 |

c. | 0.0475 |

d. | 0.0485 |

ANS: C PTS: 1

- Refer to Exhibit 5-2. The proportion of scores that lie between 460 and 600 is ____.

a. | 0.4394 |

b. | 0.5365 |

c. | 0.4406 |

d. | 0.4635 |

ANS: B PTS: 1

- Refer to Exhibit 5-2. The raw score that lies at the 90th percentile is ____.

a. | 615.20 |

b. | 384.80 |

c. | 616.10 |

d. | 383.90 |

ANS: A PTS: 1

- Refer to Exhibit 5-2. The proportion of scores between 300 and 400 is ____.

a. | 0.3665 |

b. | 0.4868 |

c. | 0.8533 |

d. | 0.1203 |

ANS: D PTS: 1

- The standard deviation of the
*z*distribution equals ____.

a. | 1 |

b. | 0 |

c. | S X |

d. | N |

ANS: A PTS: 1

- The mean of the
*z*distribution equals ____.

a. | 1 |

b. | 0 |

c. | S X |

d. | N |

ANS: B PTS: 1

- The
*z*score corresponding to the mean of a raw score distribution equals ____.

a. | the mean of the raw scores |

b. | 0 |

c. | 1 |

d. | N |

ANS: B PTS: 1

- The normal curve is ____.

a. | linear |

b. | rectangular |

c. | bell-shaped |

d. | skewed |

ANS: C PTS: 1

- In a normal curve, the inflection points occur at ____.

a. | m ± 1s |

b. | ±1s |

c. | m ± 2s |

d. | m |

ANS: A PTS: 1

- The z score corresponding to a raw score of 120 is ____.

a. | 1.2 |

b. | 2.0 |

c. | 1.0 |

d. | impossible to compute from the information given |

ANS: D PTS: 1 **Exhibit 5-3**An economics test was given and the following sample scores were recorded:

Individual |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |

Score |
12 |
12 |
7 |
10 |
9 |
12 |
13 |
8 |
9 |
8 |

- Refer to Exhibit 5-3. The mean of the distribution is ____.

a. | 12.00 |

b. | 10.00 |

c. | 9.00 |

d. | 8.00 |

ANS: B PTS: 1

- Refer to Exhibit 5-3. The standard deviation of the distribution is ____.

a. | 10.20 |

b. | 2.10 |

c. | 2.11 |

d. | 10.74 |

ANS: C PTS: 1

- Refer to Exhibit 5-3. The
*z*score for individual*D*is ____.

a. | 1 |

b. | 0 |

c. | 10 |

d. |

ANS: B PTS: 1

- Refer to Exhibit 5-3. The
*z*score for individual*E*is ____.

a. | 0.47 |

b. | 9.00 |

c. | 4.27 |

d. | -0.47 |

ANS: D PTS: 1

- Refer to Exhibit 5-3. The
*z*score for individual*G*is ____.

a. | -1.42 |

b. | 13.00 |

c. | 1.42 |

d. | 6.16 |

ANS: C PTS: 1 **Exhibit 5-4**A distribution has a mean of 60.0 and a standard deviation of 4.3.

- Refer to Exhibit 5-4. The raw score corresponding to a
*z*score of 0.00 is ____.

a. | 64.3 |

b. | 14.0 |

c. | 4.3 |

d. | 60.0 |

ANS: D PTS: 1

- Refer to Exhibit 5-4. The raw score corresponding to a
*z*score of -1.51 is ____.

a. | 53.5 |

b. | 66.5 |

c. | 66.4 |

d. | 53.6 |

ANS: A PTS: 1

- Refer to Exhibit 5-4. The raw score corresponding to a
*z*score of 2.02 is ____.

a. | 51.3 |

b. | 68.7 |

c. | 51.4 |

d. | 68.6 |

ANS: B PTS: 1

- If a population of scores is normally distributed, has a mean of 45 and a standard deviation of 6, the most extreme 5% of the scores lie beyond the score(s) of ____.

a. | 35.13 |

b. | 45.99 |

c. | 56.76 and 33.24 |

d. | 45.99 and 35.13 |

ANS: C PTS: 1

- If a distribution of raw scores is negatively skewed, transforming the raw scores into
*z*scores will result in a ____ distribution.

a. | normal |

b. | bell-shaped |

c. | positively skewed |

d. | negatively skewed |

ANS: D PTS: 1 MSC: WWW

- The mean of the
*z*distribution equals ____.

a. | 0 |

b. | 1 |

c. | N |

d. | depends on the raw scores |

ANS: A PTS: 1 MSC: WWW

- The standard deviation of the
*z*distribution equals ____.

a. | 0 |

b. | 1 |

c. | the variance of the z distribution |

d. | b and c |

ANS: D PTS: 1

- S(
*z*–*m*) equals ____._{z}

a. | 0 |

b. | 1 |

c. | the variance |

d. | cannot be determined |

ANS: A PTS: 1

- The proportion of scores less than
*z*= 0.00 is ____.

a. | 0.00 |

b. | 0.50 |

c. | 1.00 |

d. | -0.50 |

ANS: B PTS: 1

- In a normal distribution the
*z*score for the mean equals ____.

a. | 0 |

b. | the z score for the median |

c. | the z score for the mode |

d. | all of the above |

ANS: D PTS: 1 MSC: WWW

- In a normal distribution approximately ____ of the scores will fall within 1 standard deviation of the mean.

a. | 14% |

b. | 95% |

c. | 70% |

d. | 83% |

ANS: C PTS: 1

- Would you rather have an income (assume a normal distribution and you are greedy) ____?

a. | with a z score of 1.96 |

b. | in the 95th percentile |

c. | with a z score of -2.00 |

d. | with a z score of 0.000 |

ANS: A PTS: 1 MSC: WWW

- How much would your income be if its
*z*score value was 2.58?

a. | $10,000 |

b. | $ 9,999 |

c. | $ 5,000 |

d. | cannot be determined from information given |

ANS: D PTS: 1

- Which of the following
*z*scores represent(s) the most extreme value in a distribution of scores assuming they are normally distributed?

a. | 1.96 |

b. | 0.0001 |

c. | -0.0002 |

d. | -3.12 |

ANS: D PTS: 1 MSC: WWW

- Assuming the
*z*scores are normally distributed, what is the percentile rank of a*z*score of -0.47?

a. | 31.92 |

b. | 18.08 |

c. | 50.00 |

d. | 47.00 |

e. | 0.06 |

ANS: A PTS: 1 MSC: WWW

- A standardized test has a mean of 88 and a standard deviation of 12. What is the score at the 90th percentile? Assume a normal distribution.

a. | 90.00 |

b. | 112.00 |

c. | 103.36 |

d. | 91.00 |

ANS: C PTS: 1 MSC: WWW

- On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what is the percentile rank of a score of 56?

a. | 58.30 |

b. | 0.00 |

c. | 25.27 |

d. | 38.30 |

e. | 11.70 |

ANS: E PTS: 1 MSC: WWW

- On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what percentage of scores fall below a score of 83.8?

a. | 55.00 |

b. | 79.12 |

c. | 20.88 |

d. | 29.12 |

e. | 70.88 |

ANS: E PTS: 1 MSC: WWW

- On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what percentage of scores fall between 70 and 80?

a. | 75.66 |

b. | 70 23 |

c. | 24.34 |

d. | 23.57 |

e. | 12.17 |

ANS: C PTS: 1 MSC: WWW

- You have just received your psychology exam grade and you did better than the mean of the exam scores. If so, the
*z*transformed value of your grade must

a. | be greater than 1.00 |

b. | be greater than 0.00 |

c. | have a percentile rank greater than 50% |

d. | can’t determine with information given |

e. | b and c. |

ANS: E PTS: 1

- You have just taken a standardized skills test designed to help you make a career choice. Your math skills score was 63 and your writing skills score was 45. The standardized math distribution is normally distributed, with
*m*= 50, and*s*= 8. The writing skills score distribution is also normally distributed, with*m*= 30, and*s*= 10. Based on this information, as between pursuing a career that requires good math skills or one requiring good writing skills, you should chose

a. | neither, your skills are below average in both |

b. | the career requiring good math skills. |

c. | neither, this approach is bogus; dream interpretation should be used instead. |

d. | the career requiring good writing skills. |

ANS: D PTS: 1

- A distribution of raw scores is positively skewed. You want to transform it so that it is normally distributed. Your friend, who fancies herself a statistics whiz, advises you to transform the raw scores to
*z*scores; that the*z*scores will be normally distributed. You should

a. | Ignore the advice because your friend flunked her last statistics test |

b. | Ignore the advice because z distributions have the same shape as the raw scores. |

c. | Take the advice because z distributions are always normally distributed |

d. | Take the advice because z distributions are usually normally distributed |

ANS: B PTS: 1

- All bell-shaped curves

a. | are normal curves |

b. | have means = 0 |

c. | are symmetrical |

d. | a and c |

ANS: C PTS: 1

- If you transformed a set of raw scores, and then added 15 to each
*z*score, the resulting scores

a. | would have a standard deviation = 1 |

b. | would have a mean = 0 |

c. | would have a mean =15 |

d. | would have a standard deviation > 1 |

e. | a and c |

ANS: E PTS: 1

- A set of raw scores has a rectangular shape. The
*z*transformed scores for this set of raw scores has a ____ shape.

a. | rectangular |

b. | normal (bell-shaped) |

c. | it depends on the number of scores in the distribution |

d. | none of the above |

ANS: A PTS: 1

- Makaela took a Spanish exam; her grade was 79. The distribution was normally shaped with = 70 and
*s*= 12. Juan took a History exam; his grade was 86. The distribution was normally shaped with = 80 and*s*= 8. Which did better on their exam relative to those taking the exam?

a. | Makaela. |

b. | Juan. |

c. | Neither, they both did as well as each other. |

d. | Makaela, because her exam was harder |

e. | a and d. |

ANS: C PTS: 1

- Table A (Areas under the normal curve) in your textbook has no negative
*z*values, this means ____.

a. | the table can only be used with positive z values |

b. | the table can be used with both positive and negative z values because it is symmetrical |

c. | the table can be used with both positive and negative z values because it is skewed |

d. | none of the above |

ANS: B PTS: 1

- A testing service has 1000 raw scores. It wants to transform the distribution so that the mean = 10 and the standard deviation = 1. To do so, ____.

a. | Do a z transformation for each raw score and add 10 to each z score. |

b. | Do a z transformation for each raw score and multiply each by 10 |

c. | Divide the raw scores by 10 |

d. | Compute the deviation score for each raw score. Divide each deviation score by the standard deviation of the raw scores. Take this result for all scores and add 10 to each one. |

e. | a and d |

ANS: E PTS: 1

- Given the following set of sample raw scores, X: 1, 3, 4, 6, 8. What is the
*z*transformed value for the raw score of 3?

a. | -0.18 |

b. | -0.48 |

c. | -0.15 |

d. | -0.52 |

ANS: D PTS: 1 **TRUE/FALSE**

- A
*z*distribution always is normally shaped.

ANS: F PTS: 1

- All standard scores are
*z*scores.

ANS: T PTS: 1

- A
*z*score is a transformed score.

ANS: T PTS: 1

- A
*z*score designates how many standard deviations the raw score is above or below the mean.

ANS: T PTS: 1 MSC: WWW

- The
*z*distribution takes on the same shape as the raw scores.

ANS: T PTS: 1 MSC: WWW

*z*scores allow comparison of variables that are measured on different scales.

ANS: T PTS: 1

- In a normal curve, the area contained between the mean and a score that is 2.30 standard deviations above the mean is 0.4893 of the total area.

ANS: T PTS: 1

- The normal curve reaches the horizontal axis in 4 standard deviations above and below the mean.

ANS: F PTS: 1

- For any
*z*distribution of normally distributed scores,*P*_{50}is always equal to zero.

ANS: T PTS: 1 MSC: WWW

- If the original raw score distribution has a mean that is not equal to zero, the mean of the
*z*transformed scores will not equal zero either.

ANS: F PTS: 1

- It is impossible to have a
*z*score of 30.2.

ANS: F PTS: 1 MSC: WWW

- The area under the normal curve represents the proportion of scores that are contained in the area.

ANS: T PTS: 1 MSC: WWW

- If the raw score distribution is very positively skewed, the standard deviation of the
*z*transformed scores will not equal 1.

ANS: F PTS: 1

- The area beyond a
*z*score of -1.12 is the same as the area beyond a*z*score of 1.12.

ANS: T PTS: 1

- A raw score that is 1 standard deviation above the mean of the raw score distribution will have a
*z*score of 1.

ANS: T PTS: 1 **DEFINITIONS**

- Define asymptotic.

ANS:Answer not provided. PTS: 1 MSC: WWW

- Define normal curve.

ANS:Answer not provided. PTS: 1

- Define standard (
*z*) scores.

ANS:Answer not provided. PTS: 1 MSC: WWW **SHORT ANSWER**

- List three characteristics of a
*z*distribution.

ANS:Answer not provided. PTS: 1 MSC: WWW

- Is a
*z*distribution always normally shaped? Explain.

ANS:Answer not provided. PTS: 1

- Does the
*z*transformation result in a score having the same units of measurement as the raw score? Explain. Why is this advantageous?

ANS:Answer not provided. PTS: 1 MSC: WWW

- Are all bell-shaped curves normal curves? Explain.

ANS:Answer not provided. PTS: 1

- What is meant by a transformed score? Give an example.

ANS:Answer not provided. PTS: 1

- If a score is at the mean of a set of raw scores, where will it be if the set of raw scores is transformed to
*z*scores? Why?

ANS:Answer not provided. PTS: 1**Chapter 7—Linear Regression** **MULTIPLE CHOICE**

- The primary reason we use a scatter plot in linear regression is ____.

a. | to determine if the relationship is linear or curvilinear |

b. | to determine the direction of the relationship |

c. | to compute the magnitude of the relationship |

d. | to determine the slope of the least squares regression line |

ANS: A PTS: 1

- When the relation between
*X*and*Y*is imperfect, the prediction of*Y*given*X*is ____.

a. | perfect |

b. | always equal to Y |

c. | impossible to determine |

d. | approximate |

ANS: D PTS: 1

- The regression equation most often used in psychology minimizes ____.

a. | S (Y – Y’) |

b. | S (Y – Y’)^{2} |

c. | S (Y – X)^{2} |

d. | |

e. | none of the above |

ANS: B PTS: 1

- The regression of
*Y*on*X*____.

a. | predicts X given Y |

b. | predicts X’ given X |

c. | predicts Y given X |

d. | predicts Y given Y’ |

ANS: C PTS: 1

- The regression of
*X*on*Y*____.

a. | predicts Y given X |

b. | predicts Y given X |

c. | predicts X given Y |

d. | is generally the same as the regression of Y on X |

e. | c and d |

ANS: C PTS: 1

- If the correlation between two sets of scores is 0 and one had to predict the value of
*Y*for any given value of*X*, the best prediction of*Y*would be ____.

a. | b_{Y} |

b. | |

c. | 0 |

d. |

ANS: B PTS: 1

- During the past 5 years there has been an inflationary trend. Listed below is the average cost of a gallon of milk for each year.

1981 |
1982 |
1983 |
1984 |
1985 |

$1.10 |
$1.23 |
$1.30 |
$1.50 |
$1.65 |

Assuming a linear relationship exists, and that the relationship continues unchanged through 1986, what would you predict for the average cost of a gallon of milk in 1986?

a. | $1.77 |

b. | $1.72 |

c. | $1.70 |

d. | $1.83 |

ANS: A PTS: 1 **Exhibit 7-1**A researcher collects data on the relationship between the amount of daily exercise an individual gets and the percent body fat of the individual. The following scores are recorded.

Individual |
1 |
2 |
3 |
4 |
5 |

Exercise (min) |
10 |
18 |
26 |
33 |
44 |

% Fat |
30 |
25 |
18 |
17 |
14 |

- Refer to Exhibit 7-1. Assuming a linear relationship holds, the least squares regression line for predicting % fat from the amount of exercise an individual gets is ____.

a. | Y’ = 0.476X + 33.272 |

b. | Y’ = 1.931X + 66.363 |

c. | Y’ = -0.476X + 33.272 |

d. | Y’ = -0.432X + 32.856 |

ANS: C PTS: 1

- Refer to Exhibit 7-1. If an individual exercises 20 minutes daily, his predicted % body fat would be ____.

a. | 21.63 |

b. | 27.74 |

c. | 27.88 |

d. | 23.75 |

ANS: D PTS: 1

- Refer to Exhibit 7-1. The least squares regression line for predicting the amount of exercise from % fat is ____.

a. | X’ = -1.931Y + 66.363 |

b. | X’ = -0.476Y + 33.272 |

c. | X’ = 1.931Y + 66.363 |

d. | X’ = -1.905Y + 62.325 |

ANS: A PTS: 1

- Refer to Exhibit 7-1. If an individual has 22% fat, his predicted amount of daily exercise is ____.

a. | 22.80 |

b. | 23.88 |

c. | 24.76 |

d. | 20.22 |

ANS: B PTS: 1

- Refer to Exhibit 7-1. The value for the standard error of estimate in predicting % fat from daily exercise is ____.

a. | 3.35 |

b. | 4.32 |

c. | 2.14 |

d. | 1.66 |

e. | none of the above |

ANS: C PTS: 1

- The assumption of homoscedasticity is that ____.

a. | the range of the Y scores is the same as the X scores |

b. | the X and Y distributions have the same mean values |

c. | the variability of Y doesn’t change over the X scores |

d. | the variability of the X and Y distributions is the same |

ANS: C PTS: 1

- You go to a carnival and a sideshow performer wants to bet you $100 that he can guess your exact weight just from knowing your height. It turns out that there is the following relationship between height and weight.

Height (in) |
60.0 |
62.0 |
63.0 |
66.5 |
73.5 |
84.0 |

Weight (lbs) |
99 |
107 |
111 |
125 |
153 |
195 |

Should you accept the performer’s bet? Explain.

a. | yes |

b. | need more information |

c. | no |

d. | yes, if he measures my height in centimeters |

ANS: C PTS: 1

- If
*r*= 0.4582,*s*= 3.4383, and_{Y}*s*= 5.2165, the value of_{X}*b*= ____._{Y}

a. | 0.695 |

b. | 0.458 |

c. | 0.302 |

d. | 1 – 0.458 |

e. | none of the above |

ANS: C PTS: 1

- In multiple regression, if the second predictor variable correlates highly with the predicted variable, than it is quite likely that ____.

a. | R^{2} = 1.00 |

b. | R^{2} > r^{2} |

c. | R^{2} = r^{2} |

d. | R^{2} < r^{2} |

ANS: B PTS: 1

- If the relationship between
*X*and*Y*is perfect:

a. | r = b |

b. | the equation for Y‘ equals the equation for X‘ |

c. | prediction is approximate |

d. | a and b |

e. | all of the above |

ANS: D PTS: 1

- When predicting
*Y*, adding a second predictor variable to the first predictor variable*X*, will ____.

a. | always increase prediction accuracy |

b. | increase prediction accuracy depending on the relationship between the second predictor variable and X |

c. | Increase prediction accuracy depending on the relationship between the second predictor variable and Y |

d. | b and c |

ANS: D PTS: 1

- The higher the standard error of estimate is,

a. | the more accurate the prediction is likely to be |

b. | the less accurate is the prediction is likely to be |

c. | the less confidence we have in the accuracy of the prediction |

d. | the more confidence we have in the accuracy of the prediction |

e. | a and d |

f. | b and c |

ANS: F PTS: 1

- If
*s*= 0.0 the relationship between the variables is ____._{Y|X}

a. | perfect |

b. | imperfect |

c. | curvilinear |

d. | unknown |

ANS: A PTS: 1 MSC: WWW

- S (
*Y*–*Y’*) equals ____.

a. | 0 |

b. | 1 |

c. | cannot be determined from information given |

d. | who cares |

ANS: A PTS: 1

- S (
*Y*–*Y’*)^{2}represents ____.

a. | the standard deviation |

b. | the variance |

c. | the standard error of estimate |

d. | the total error of prediction |

ANS: D PTS: 1 MSC: WWW

- In a particular relationship
*N*= 80. How many points would you expect on the average to find within ±1*s*of the regression line?_{Y|X}

a. | 40 |

b. | 80 |

c. | 54 |

d. | 0 |

ANS: C PTS: 1

- What would you predict for the value of
*Y*for the point where the value of*X*is ?

a. | cannot be determined from information given |

b. | 0 |

c. | 1 |

d. |

ANS: D PTS: 1

- If the value of
*s*= 4.00 for relationship_{Y|X}*A*and*s*= 5.25 for relationship_{Y|X}*B*, in which relationship would you have the most confidence in a particular prediction?

a. | A |

b. | B |

c. | it makes no difference |

d. | cannot be determined from information given |

ANS: A PTS: 1 MSC: WWW

- If
*b*is negative, higher values of_{Y}*X*are associated with ____.

a. | lower values of X’ |

b. | higher values of Y |

c. | higher values of (Y – Y’) |

d. | lower values of Y |

ANS: D PTS: 1

- Which of the following statement(s) is (are) an important consideration(s) in applying linear regression techniques?

a. | the relationship should be linear |

b. | both variables must be measured in the same units |

c. | predictions for Y should be within the range of the X variable in the sample |

d. | a and c |

ANS: D PTS: 1 MSC: WWW

- In the regression equation
*Y’*=*X*, the*Y*-intercept is ____.

a. | |

b. | |

c. | 0 |

d. | 1 |

ANS: C PTS: 1

- If the value for
*a*is negative, the relationship between_{Y}*X*and*Y*is ____.

a. | positive |

b. | negative |

c. | inverse |

d. | cannot be determined from information given |

ANS: D PTS: 1 MSC: WWW

- If
*b*= 0, the regression line is ____._{Y}

a. | horizontal |

b. | vertical |

c. | undefined |

d. | at a 45° angle to the X axis |

ANS: A PTS: 1

- The least-squares regression line minimizes ____.

a. | s |

b. | s_{Y|X} |

c. | S (Y – )^{2} |

d. | S (Y – Y’)^{2} |

e. | b and d |

ANS: E PTS: 1

- The points (0,5) and (5,10) fall on the regression line for a perfect positive linear relationship. What is the regression equation for this relationship?

a. | Y’ = X + 5 |

b. | Y’ = 5X |

c. | Y’ = 5X + 10 |

d. | cannot be determined from information given. |

ANS: A PTS: 1

- For the following points what would you predict to be the value of
*Y’*when*X*= 19? Assume a linear relationship.

X |
6 |
12 |
30 |
40 |

Y |
10 |
14 |
20 |
27 |

** **

a. | 16.35 |

b. | 24.69 |

c. | 22.00 |

d. | 17.75 |

ANS: A PTS: 1 MSC: WWW

- If
*N*= 8, S*X*= 160, S*X*^{2}= 4656, S*Y*= 79, S*Y*^{2}= 1309, and S*XY*= 2430, what is the value of*b*?_{Y}

a. | 0.9217 |

b. | -1.8010 |

c. | 0.5838 |

d. | 0.7922 |

ANS: C PTS: 1

- If
*X*and*Y*are transformed into*z*scores, and the slope of the regression line of the*z*scores is -0.80, what is the value of the correlation coefficient?

a. | -0.80 |

b. | 0.80 |

c. | 0.40 |

d. | -0.40 |

ANS: A PTS: 1 MSC: WWW

- If the regression equation for a set of data is
*Y’*= 2.650*X*+ 11.250 then the value of*Y’*for*X*= 33 is ____.

a. | 87.45 |

b. | 371.25 |

c. | 98.70 |

d. | 76.20 |

ANS: C PTS: 1 MSC: WWW

- If = 57.2, = 84.6, and
*b*= 0.37, the value of_{Y}*a*= ____._{Y}

a. | 141.80 |

b. | -25.90 |

c. | 63.44 |

d. | 27.40 |

ANS: C PTS: 1

- If the regression line for predicting
*X*given*Y*were*X’*= 103*Y*+ 26.2, what would the value of*X’*be if*Y*= 0.2?

a. | 129.2 |

b. | 25.8 |

c. | 5.2 |

d. | 46.8 |

ANS: D PTS: 1

- If
*s*=_{Y}*s*= 1 and the value of_{X}*b*= 0.6, what will the value of_{Y}*r*be?

a. | 0.36 |

b. | 0.60 |

c. | 1.00 |

d. | 0.00 |

ANS: B PTS: 1

- When using more than one predictor variable, ____ tells us the proportion of variance accounted for by the predictor variables.

a. | r |

b. | SS_{X} |

c. | SS_{Y} |

d. | R^{2} |

ANS: D PTS: 1 MSC: WWW

- Which of the following statements is(are) false?

a. | b_{Y} is the slope of the line for minimizing errors in predicting Y. |

b. | a_{Y} is the Y axis intercept for minimizing errors in predicting Y. |

c. | s_{Y}_{½} is the standard error of estimate for predicting _{X}Y given X. |

d. | All of the above statements are true. |

e. | R^{2} is the multiple coefficient of nondetermination. |

ANS: E PTS: 1 MSC: WWW

- The regression coefficient
*b*_{Y}and the correlation coefficient*r*____.

a. | necessarily increase in magnitude as the strength of relationship increases |

b. | are both slopes of straight lines |

c. | are not related |

d. | will equal each other when the variability of the X and Y distributions are equal |

e. | b and d |

ANS: E PTS: 1

- When predicting
*Y*given*X*, ____.

a. | the prediction is valid only within the range of X |

b. | the variability of the Y values over the range of the X values should be the same |

c. | the representativeness of the sample used to derive the regression line is an important consideration |

d. | a, b, and c |

e. | a and c |

ANS: D PTS: 1

- When predicting
*Y*from two variables relative to using only one variable, ____.

a. | prediction accuracy always increases |

b. | prediction accuracy is dependent on the relationship between the second variable and the Y variable |

c. | increase in prediction accuracy depends on the correlation between the two predictor variables |

d. | b and c |

ANS: D PTS: 1

- There is ____ between the
*s*and_{Y|X}*r*.

a. | a direct relationship |

b. | an inverse relationship |

c. | no relationship |

d. | animosity |

ANS: B PTS: 1

- The regression coefficient for predicting
*Y*given*X*is symbolized by ____

a. | b_{Y} |

b. | a_{Y} |

c. | b_{X} |

d. | a_{X} |

ANS: A PTS: 1

- The regression coefficient for predicting
*X*given*Y*is symbolized by ____.

a. | b_{Y} |

b. | a_{Y} |

c. | b_{X} |

d. | a_{X} |

ANS: C PTS: 1

- The regression constant for predicting
*Y*given*X*is symbolized by ____.

a. | b_{Y} |

b. | a_{Y} |

c. | b_{X} |

d. | a_{X} |

ANS: B PTS: 1

- The regression constant for predicting
*X*given*Y*is symbolized by ____.

a. | b_{Y} |

b. | a_{Y} |

c. | b_{X} |

d. | a_{X} |

ANS: D PTS: 1

- The symbol for the standard error of estimate when predicting
*Y*given*X*is ____.

a. | r_{X|Y} |

b. | s_{X|Y} |

c. | r_{Y|X} |

d. | s_{Y|X} |

ANS: D PTS: 1 **TRUE/FALSE**

- The total error in prediction equals S (
*Y*–*Y’*).

ANS: F PTS: 1 MSC: WWW

- In general, the regression line for predicting
*X*given*Y*is the same as the regression line for predicting*Y*given*X.*

ANS: F PTS: 1

- An imperfect relationship generally yields exact prediction.

ANS: F PTS: 1

- When the relationship is perfect, the regression of
*Y*on*X*is the same as the regression of*X*on*Y.*

ANS: T PTS: 1 MSC: WWW

- Properly speaking, we should limit our predictions to the range of the base data.

ANS: T PTS: 1

- The least squares regression line insures the maximum number of direct hits.

ANS: F PTS: 1 MSC: WWW

- To do linear regression, there must be paired scores on two variables.

ANS: T PTS: 1

- If the standard deviations of the
*X*and*Y*distributions are equal, then*r*=*b*._{Y}

ANS: T PTS: 1

- If
*s*=_{X}*s*then_{Y}*b*=_{X}*b*._{Y}

ANS: T PTS: 1 MSC: WWW

- The higher the
*r*value, the lower the standard error of estimate.

ANS: T PTS: 1 MSC: WWW

- Multiple regression uses more than one predictor variable.

ANS: T PTS: 1

- Multiple regression always results in greater prediction accuracy than simple regression.

ANS: F PTS: 1

- If the correlation between two variables is 1.00, the standard error of estimate equals 0.

ANS: T PTS: 1

- Pearson
*r*is the slope of the least squares regression line when the scores are plotted as*z*scores.

ANS: T PTS: 1

- When there are two predictor variables,
*R*^{2}is the simple sum of*r*^{2}for the relationship of the first predictor variable and*Y*and*r*^{2}for the relationship of the second predictor variable and*Y*.

ANS: F PTS: 1 **DEFINITIONS**

- Define Homoscedasticity.

ANS:Answer not provided. PTS: 1

- Define least-squares regression line.

ANS:Answer not provided. PTS: 1 MSC: WWW

- Define multiple coefficient of determination.

ANS:Answer not provided. PTS: 1

- Define multiple correlation.

ANS:Answer not provided. PTS: 1

- Define regression.

ANS:Answer not provided. PTS: 1

- Define regression constant.

ANS:Answer not provided. PTS: 1

- Define regression line.

ANS:Answer not provided. PTS: 1

- Define regression of
*X*on*Y*.

ANS:Answer not provided. PTS: 1 MSC: WWW

- Define regression of
*Y*on*X.*

ANS:Answer not provided. PTS: 1

- Define standard error of estimate.

ANS:Answer not provided. PTS: 1 **SHORT ANSWER**

- Why is it important to know the standard error of estimate for a set of paired scores?

ANS:Answer not provided. PTS: 1

- Why does the least squares regression line minimize S (
*Y*–*Y’*)^{2}, rather than S (*Y*–*Y’*)?

ANS:Answer not provided. PTS: 1 MSC: WWW

- Is it true that, generally, the regression lines for predicting
*Y*given*X*and*X*given*Y*, are not the same? Explain.

ANS:Answer not provided. PTS: 1

- The least squares regression line is the prediction line that results in the most direct “hits.” Is this true? Explain.

ANS:Answer not provided. PTS: 1

- In what situation would the regression line for predicting
*Y*given*X*be the same as the line predicting*X*given*Y*? Explain.

ANS:Answer not provided. PTS: 1

- In multiple regression, will use of a second predictor variable always increase the accuracy of prediction? Explain.

ANS:Answer not provided. PTS: 1 MSC: WWW

- If there is no relationship between the
*X*and*Y*variables and we desire to predict*Y*given*X*using a least-squares criterion, it is best to predict for every*Y*score. Is this correct? If so, explain why. (Hint: one of the properties of the mean might be helpful here)

ANS:Answer not provided. PTS: 1 MSC: WWW

- A friend that thinks a lot about statistics asserts that, “the closer the points in the scatter plot are to the least-squares regression line, the higher the correlation.” Is your friend correct? Discuss.

ANS:Answer not provided. PTS: 1