Statistics for Behavioral Science Unit 2

B) s^2

Which of the following symbols identifies the sample variance? A) s B) s^2 C) σ D) σ^2

D) 16

. A population of N = 100 scores has mean µ = 30 and standard deviation σ = 4. What is the population variance? A) 2 B) 4 C) 8 D) 16

D) 14/43

. If you are randomly selecting one student from a class of 14 males and 29 females, what is the probably of selecting a male? A) 50/50 B) 14/29 C) 29/43 D) 14/43

B) far above average

. In N = 25 games last season, a college basketball team averaged µ = 76 points with a standard deviation of σ = 6. In their final game of the season, the team scored 89 points. Based on this information, the number of points scored in the final game was _____. A) a little above average B) far above average C) above average, but it is impossible to describe how much above average D) impossible to determine because there is not enough information

A) 4

. The value of SS (sum of squared deviations) is 20 for a population of N = 5 scores. What is the variance for this population? A) 4 B) 5 C) 80 D) 100

A) z = +0.50

. Which of the following z-score values represents the location closest to the mean? A) z = +0.50 B) z = +1.00 C) z = -1.00 D) z = -2.00

A) 15/90

A jar contains 50 red marbles, 25 blue marbles, and 15 black marbles. If you take a random sample of n = 3 marbles from this jar, and the first two marbles are both blue, what is the probability that the third marble will be black? A) 15/90 B) 1/90 C) 15/88 D) 1/88

p(X > 83): z-score: z= 0.25 Probability: p= 0.1013 p(X < 74): z-score: z=-0.50 Probability: p= 0.3085 p(X < 92): z-score: z= 1.00 Probability: p=0.8413 p(X > 62): z-score: -1.50 Probability: p= 0.9332 p(71 < X < 89): z-score: -0.75 > z < 0.75 Probability: p= 5468 p(65 > X > 95): z-score: -1.25 > z < 1.25 Probability: p= 0.2113

A normal distribution has a mean of µ = 80 with σ = 12. Find the following zscores and probabilities: p(X > 83): z-score: Probability: p(X < 74): z-score: Probability: p(X < 92): z-score: Probability: p(X > 62): z-score: Probability: p(71 < X < 89): z-score: Probability: p(65 > X > 95): z-score: Probability:

C) 12 points above the mean

A population distribution has σ = 6. What position in this distribution is identified by a z-score of z = +2.00? A) 2 points above the mean B) 2 points below the mean C) 12 points above the mean D) 12 points below the mean

A) 20

A population of N = 5 scores has ΣX = 20 and ΣX2 = 100. For this population, what is the value of SS (sum of squared deviations)? A) 20 B) 80 C) 100 D) 380

C) 30

A population of N = 6 scores has ΣX = 12 and ΣX2 = 54. For this population, what is the value of SS (sum of squared deviations)? A) 5 B) 9 C) 30 D) 54

X = 63: z = -0.50 X = 45 X = 65: z = -0.40 X = 46 X = 77: z = 0.20 X = 52 X = 83: z = 0.50 X = 55

A population of score with µ = 73 and σ = 20 is standardized to create a new population with µ = 50 and σ = 10. What is the new value for each of the following scores from the original population? Scores: 63, 65, 77, 83 X = 63: z = X = X = 65: z = X = X = 77: z = X = X = 83: z = X =

D) all of the above.

A random sample requires that A) every individual has an equal chance of being selected. B) the probabilities cannot change during a series selections. C) there must be sampling with replacement. D) all of the above.

A) 3

A sample of n = 25 scores has mean M = 20 and variance s2 = 9. What is the sample standard deviation? A) 3 B) 4.5 C) 9 D) 81

C) s^2 = 10; σ^2 = 9

A set of 10 scores has SS = 90. If the scores are a sample, the sample variance is _____ and if the scores are a population, the population variance is _____. A) s^2 = 9; σ^2 = 9 B) s^2 = 9; σ^2 = 10 C) s^2 = 10; σ^2 = 9 D) s^2 = 10; σ^2 = 10

z = +2.00: Tail: Right Proportion: p= 0.0228 z = +0.75: Tail: Right Proportion: p= 0.2266 z = -0.50: Tail: Left Proportion: p= 0.3085 z = -1.25: Tail: Left Proportion: p= 0.1056

Assume that a vertical line is drawn through a normal distribution at each of the following z-score locations. In each case, determine whether the tail is on the left side or the right side of the line and find the proportion of the distribution that is located in each tail. z = +2.00: Tail: Proportion: z = +0.75: Tail: Proportion: z = -0.50: Tail: Proportion: z = -1.25: Tail: Proportion:

1. the highest 15% and the rest of the scores? z= 1.05 2. the highest 40% and the rest of the scores? z= 0.25 3. the lowest 30% and the rest of the scores? z=-0.52 4. the lowest 10% and the rest of the scores? z= -1.28

For a normal distribution, what z-score forms the boundary between: 1. the highest 15% and the rest of the scores? 2. the highest 40% and the rest of the scores? 3. the lowest 30% and the rest of the scores? 4. the lowest 10% and the rest of the scores?

B) between 4 and 11

For a particular sample size of n = 10 scores, the largest distance (deviation) between a score and the mean is 11 points. The smallest distance (deviation) between a score and the mean is 4 points. Therefore, the standard deviation will be _____. A) less than 4 B) between 4 and 11 C) greater than 11 D) equal to 0

X = 45: z = -0.5 X = 60: z = +1.00 X = 30: z = -2.00 X = 65: z = +1.50

For a population with µ = 50 and σ = 10, find the z-score corresponding to each of the following X values: 45, 60, 30, 65. X = 45: z = X = 60: z = X = 30: z = X = 65: z =

z = -0.50: X = 54 z = -1.50: X = 42 z = +1.25: X = 75 z = +2.00: X = 84

For a population with µ = 60 and σ = 12, find the X value that corresponds to each of the following z-scores: -0.50, -1.50, +1.25, +2.00. z = -0.50: X = z = -1.50: X = z = +1.25: X = z = +2.00: X =

C) 15

For a sample of n = 16 scores, how many scores are used to calculate the sample variance? A) 2 B) 8 C) 15 D) 16

A) 0

For any distribution, what is the z-score corresponding to the mean? A) 0 B) 1 C) N D) Z

A) z = -0.39

For any normal distribution, what z-score separates the highest 65% of the scores from the rest of the distribution? A) z = -0.39 B) z = 0.39 C) z = 1.28 D) z = -1.28

A) 0 and 1

If an entire population with µ = 60 and σ = 8 is transformed into z-scores, then the distribution of z-scores will have a mean of _____ and a standard deviation of ____. A) 0 and 1 B) 60 and 1 C) 0 and 8 D) 60 and 8 (unchanged)

B) 12

In a population of N = 10 scores, the smallest score is X = 8 and the largest score is X = 20. Using the concept of real limits, what is the range for this population? A) 11 B) 12 C) 13 D) 20

D) History

Last week, you had exams in Math, Chemistry, English, and History. On the Math exam, the mean was µ = 35 with σ = 6 and you had a score of X = 41. On the Chemistry exam, the mean was µ = 70 with σ = 10 and you had a score of X = 50. On the English exam, the mean was µ = 75 with σ = 8 and you had a score of X = 71. On the History exam, the mean was µ = 80 with σ = 4 and you had a score of X = 86. For which class should you expect the better grade? A) Math B) Chemistry C) English D) History

Nick: X value: 65 z-score: -1.50 Rank: 3 Jess: X value: 71 z-score: -0.50 Rank: 2 Winston: X value: 80 z-score: -1.00 Rank: 1

On a History exam with µ = 74 and σ = 6, Nick scored 9 points below the mean, Jess had a score of X = 71, and Winston had a z-score of z = -1.00. For each student, find their exam score (X value), their z-score, and rank them in order from highest grade (1) to lowest grade (3). X value z-score Rank Nick: -X value: z-score: Rank: Jess: -X value: z-score: Rank: Winston: -X value: z-score: Rank:

D) all of the above

Probably values are always _____. A) greater than or equal to 0 B) less than or equal to 1 C) positive numbers D) all of the above

B) 2.50%

Scores on the SAT form a normal distribution with µ = 500 with σ = 100. What is the minimum SAT score needed to be in the top 25% of the distribution? A) X = 433 B) X = 567 C) X = 525 D) X = 475

D) raw scores.

The direct, unchanged scores that are the direct result of measurement are called A) standardized scores. B) deviation scores. C) z-scores. D) raw scores.

D) 0.06681

The proportion of a normal distribution that corresponds to values greater than z =1.50 is p = 0.06681. What is the proportion that corresponds to values less than z = -1.00? A) 0.93319 B) -0.93319 C) -0.06681 D) 0.06681

D) When the population standard deviation is much smaller than 15.

Under what circumstances is a score that is 15 points above the mean an extreme score relatively far from the mean? A) When the population mean is much larger than 15. B) When the population standard deviation is much larger than 15. C) When the population mean is much smaller than 15. D) When the population standard deviation is much smaller than 15.

D) When the population standard deviation is much greater than 5.

Under what circumstances is a score that is located 5 points above the mean a central value, relatively close to the mean? A) When the population mean is much less than 5. B) When the population mean is much greater than 5. C) When the population standard deviation is much less than 5. D) When the population standard deviation is much greater than 5.

A) SS = B) σ^2 = C) σ =

Using the definitional formula, compute the SS, variance, and standard deviation for the following population of scores. Scores: 5, 10, 9, 3, 4, 5 A) SS = B) σ^2 = C) σ =

A) SS = 18; variance = 6

What are the values for SS and variance for the following sample of n = 3 scores? Sample: 1, 4, 7 A) SS = 18; variance = 6 B) SS = 18; variance = 9 C) SS = 66; variance = 22 D) SS = 66; variance = 33

C) 1.5

What is the variance for the following population of scores? Scores: 5, 2, 5, 4 A) 6 B) 2 C) 1.5 D) 1.22

B) 2.50%

What percentage of a normal distribution is located in the tail beyond z = 1.96? A) 1.25% B) 2.50% C) 15.87% D) 97.50%

B) Above the mean by a distance equal to 2 standard deviations

What position in the distribution corresponds to a z-score of z = +2.00? A) Above the mean by 2 points. B) Above the mean by a distance equal to 2 standard deviations. C) Below the mean by 2 points. D) Below the mean by a distance equal to 2 standard deviations.

D) 0.4394

What proportion of a normal distribution is located between the mean and z = -1.55? A) 0.0606 B) -0.9394 C) -0.4394 D) 0.4394

A) 0.3829

What proportion of a normal distribution is located between z = -0.50 and z = +0.50? A) 0.3829 B) 0.3085 C) 0.6915 D) 0.1915

C) 0.9199

What proportion of a normal distribution is located between z = -1.75 and z = +1.75? A) 0.0401 B) 0.0668 C) 0.9199 D) 0.4599

C) z = ±0.68

What z-score values form the boundaries form the middle 50% of a normal distribution? A) z = ±0.25 B) z = ±0.39 C) z = ±0.68 D) z = ±0.84

D) None of these options are an advantage.

Which of the following is an advantage of transforming X values into z-scores? A) All negative numbers are eliminated. B) The distribution is transformed into a normal shape. C) All scores are moved closer to the mean. D) None of these options are an advantage.

A) x - µ

Which of the following represents the deviation score? A) x - µ B) Z C) s D) (x - µ)/s

C) σ

Which of the following symbols identifies the population standard deviation? A) s B) s^2 C) σ D) σ^2