Intro Stat Test 2 (PSY 2301)

For a normal population with a mean of µ = 80 and a standard deviation of σ = 10, what is the probability of obtaining a random sample of n = 25 scores with the mean greater than M = 85? A. 0.0062 or 0.62% B. 0.9938 or 99.38% C. 0.3085 or 30.85% D. 0.6915 or 69.15% E. none of the above

A. 0.0062 or 0.62%

A sample of n = 81 is randomly selected from a population with μ = 50 with σ = 18. On average, how much error (i.e., difference) is reasonable to expect between the sample mean and the population mean? A. 2 points B. 5 points C. 10 points D. 18 points E. none of the above

A. 2 points

On an exam with M = 70, you have a score of X = 80. Which value of the standard deviation would give you the highest position in the class distribution? A. s = 5 B. s = 8 C. s = 10 D. s = 12 E. can't be determined from the information given

A. s = 5

For a population with µ = 56 and σ = 8, what is the z-score corresponding to X = 52? A. z = -0.50 B. z = 0.50 C. z = -2.0 D. z = 1.50

A. z = -0.50

For a population with µ = 10 and σ = 4, what is the z-score corresponding to X = 13? A. z = 0.75 B. z = .50 C. z = -1.00 D. z = -0.50 E. none of the above

A. z = 0.75

A normal distribution of scores in population has a mean of µ = 150 with σ = 25. A. What is the probability of randomly selecting a score greater than X = 160 from this population? B. If a sample of n = 100 is randomly selected from this population, what is the probability that the sample mean will be greater than M = 160?

A: Compute the z-score that corresponds to X = 160: z = (X - µ)/ σ = (160 - 150)/25 = 0.40 In the Unit Normal table find that the proportion of scores above z = 0.40 (i.e., in the tail of distribution, column C) equals 0.3446. Therefore, the probability of randomly selecting a score greater than X = 160 is 34.46%. B: Compute standard error σM of the sampling distribution for the samples of n = 100 σM = σ/SqRoot of n = 25/sq.Root of 100 = 25/10 = 2.5 Compute the z-score that corresponds to M = 160: z = (M - µ)/ σM = (160 - 150)/2.5= 10/2.5 = 4.0 In the Unit Normal table find that the proportion above z = 4.0 (i.e., in the tail of distribution, column C) equals 0.00003. Therefore, the probability of randomly selecting a sample with the mean greater than M = 160 is 0.003%.

What proportion of a normal distribution is located between the mean and z = 1.30? A. 0.0107 B. 0.4032 C. 0.0968 D. 0.4893 E. none of the above

B. 0.4032

For a population with µ = 300 and σ = 20, what is the X value corresponding to z = 1.50? A. X = 320 B. X = 330 C. X = 340 D. X = 430 E. none of the above

B. X = 330

For a sample with M = 40 and s = 16, what is the X value corresponding to z = - 0.25? A. X = 37 B. X = 36 C. X = 32 D. X = 30 E. none of the above

B. X = 36

What position in the distribution corresponds to a z-score of z = - 1.5? A. above the mean by 1.5 points B. below the mean by a distance equal to 1.5 standard deviation C. above the mean by a distance equal to 1.5 standard deviation D. below the mean by 1.5 points

B. below the mean by a distance equal to 1.5 standard deviation

Which of the following z-scores correspond to a score that is below the mean by 2 standard deviations? A. z = -1.50 B. z = -2.00 C. z = -3.00 D. can't be determined without knowing the value of standard deviation

B. z = -2.00

For a population with a standard deviation of 8, what is the z-score corresponding to a score that is 4 points above the mean? A. z = 1.0 B. z = 0.5 C. z = 4 D. z = -0.5 E. none of the above

B. z = 0.5

IQ scores form a normal distribution with µ = 100 and σ = 15. Individuals with IQs above 140 are classified in the genius category. What proportion of the population consists of geniuses? A. 0.0023 B. 0.0678 C. 0.0038 D. 0.0347 E. none of the above

C. 0.0038

A normal distribution has μ = 40 and σ = 4. What is the probability of randomly selecting a score smaller than 35 from this distribution? A. 0.7734 or 77.34% B. 0.8944 or 89.44% C. 0.1056 or 10.56% D. 0.4532 or 45.32% E. none of the above

C. 0.1056 or 10.56%

A class consists of 60 males and 40 females. A random sample of n = 10 students is selected. If the first four randomly selected students were all females, what is the probability that the fifth student will be a female? A. 0.20 or 20% B. 0.52 or 52% C. 0.40 or 40% D. 0.30 or 30% E. none of the above

C. 0.40 or 40%

What proportion of a normal distribution is located between the mean and z = - 1.75? A. 0.8849 B. -0.1151 C. 0.4599 D. -0.4599 E. none of the above

C. 0.4599

What proportion of a normal distribution is located in the body, below z = 1.25? A. 0.9332 B. 0.1056 C. 0.8944 D. 0.1336 E. none of the above

C. 0.8944

A normal distribution has μ = 40 and σ = 4. What is the probability of randomly selecting a score smaller than 45 from this distribution? A. 0.0062 or 0.62% B. 0.3944 or 39.44% C. 0.8944 or 89.44% D. 0.1056 or 10.56% E. none of the above

C. 0.8944 or 89.44%

What is the probability of randomly selecting a z-score less than z = 1.55 from a normal distribution? A. 0.8944 or 89.44% B. 0.0606 or 6.06% C. 0.9394 or 93.94% D. 0.4394 or 43.94% E. none of the above

C. 0.9394 or 93.94%

Last week, Sarah had exams in English and in Biology. On the English exam, the mean was µ = 50 with σ = 5 and Sarah had a score of X = 55. On the Biology exam, the mean was µ=60 with σ = 10, and Sarah had a score of X = 70. In which class Sarah's performance was better based on this outcomes? A. English B. Biology C. Sarah did equally well in both classes D. There is not enough information to determine which is the better exam result

C. Sarah did equally well in both classes

For an exam with a mean of M = 80 and a standard deviation of s = 6, Mary has a score of X = 88, Bob's score corresponds to z = +1.5, and Sue's score is located above the mean by 10 points. If the students are placed in order from highest score to lowest score, what is the correct order? A. Bob, Mary, Sue B. Sue, Mary, Bob C. Sue, Bob, Mary D. Mary, Sue, Bob E. none of the above is correct

C. Sue, Bob, Mary

A distribution of exam scores is positively skewed with M = 55 and s = 5. If these students' scores are transformed into z-scores, what is the shape of z-scores distribution? A. The z-scores distribution is symmetrical B. The z-scores distribution is negatively skewed C. The z-scores distribution is positively skewed D. Can't be determined without additional information

C. The z-scores distribution is positively skewed

For a population with µ = 10 and σ = 2, what is the X value corresponding to z = 2.5? A. X = 20 B. X = 14 C. X = 15 D. X = 5 E. none of the above

C. X = 15

For a population with µ = 60 and σ = 4, what is the X value corresponding to z = - 2.00? A. X = 76 B. X = 68 C. X = 52 D. X = 44 E. none of the above

C. X = 52

Which of the following z-scores represent the location closest to the mean? A. z = 2.5 B. z = -2.75 C. z = -.25 D. z = 1.20 E. z = 0.35

C. z = -.25

A random sample of n = 16 scores is obtained from a population with a mean of µ = 60 and a standard deviation of σ = 10. If the sample mean is M = 55, what is the z-score for the sample mean? A. z = 2.5 B. z = 2.0 C. z = -2.0 D. z = -1.0 E. none of the above

C. z = -2.0

What z-score value separates the highest 15% of the scores in a normal distribution from the lower 85%? (Note: use the closest value to the top 15% listed in the Un Normal table) A. z = 1.28 B. z = 2.17 C. z = 1.04 D. z = 0.25 E. none of the above

C. z = 1.04

A sample of n = 20 scores has a mean of M = 25 and a standard deviation of s = 4. In this sample, what is the z-score corresponding to X = 30? A. z = 5 B. z = 2.5 C. z = 1.25 D. z = 0.75 E. none of the above

C. z = 1.25

For a population wit µ = 40 and σ = 4, what is the z-score corresponding to X = 46? A. z = 1.0 B. z = -1.5 C. z = 1.5 D. z = -1.75 E. none of the above

C. z = 1.5

A population has µ= 20. What value of standard deviation would make a score X = 25 an extreme value, out in the positive tail of the distribution? A. σ = 10 B. σ = 5 C. σ = 2 D. can't be determined from the information given

C. σ = 2

A population has µ = 50. What value of standard deviation would make X = 45 a central (average) score in the population ? A. σ = 2 B. σ = 4 C. σ = 5 D. σ = 10 E. can't be determined from the information given

C. σ = 5

A normal distribution has a mean of µ = 50 with σ = 5. If one score is randomly selected from this distribution, what is the probability that the score will be less than X = 35? A. 0.7734 or 77.34% B. 0.2266 or 22.66% C. 0.4987 or 49.87% D. 0.0013 or 0.13% E. none of the above

D. 0.0013 or 0.13%

What proportion of a normal distribution is located in the tail below z = - 1.5? A. 0.1587 B. 0.9332 C. -0.0668 D. 0.0668 E. none of the above

D. 0.0668

What is the probability of randomly selecting a z-score greater than z = 0.50 from a normal distribution? A. 0.7734 or 77.34% B. 0.2266 or 22.66% C. 0.6915 or 69.15% D. 0.3085 or 30.85% E. none of the above

D. 0.3085 or 30.85%

A class consists of 75 females and 50 males. If one student is randomly selected from the class, what is the probability of selecting a male? A. 0.33 or 33% B. 0.60 or 60% C. 0.25 or 25% D. 0.40 or 40% E. none of the above

D. 0.40 or 40%

If all scores in a population with µ = 100 and σ = 10 are transformed into z-scores, than the distribution of z-scores will have a mean of _____ and a standard deviation of _____. A. 100; 1 B. 100; 10 C. 1; 0 D. 0; 1 E. can't be determined without additional information

D. 0; 1

A normal distribution of scores in population has µ = 500 and σ = 60. The distribution of sample means for samples of n = 36 randomly selected from this population will have an expected value of M equal ______ and a standard error equal _______. A. 500; 20 B. 50; 30 C. 50; 60 D. 500; 10 E. none of the above

D. 500; 10

Which of the following is a requirement for a random sample? A. Every individual has an *equal chance* of being selected B. The *probabilities cannot change* during a series of selections C. There *must be sampling with replacement* D. All of the above

D. All of the above

Under what circumstances will the distribution of sample means have a normal distribution shape? A. It will always have a normal distribution shape B. Only if the population distribution has a normal shape C. Only if the sample size is greater than 30 D. If the population distribution has a normal shape or if the sample size is greater than 30

D. If the population distribution has a normal shape or if the sample size is greater than 30

A sample is randomly selected from a normal population with μ = 50 and σ = 12. Which of the following samples would be considered extreme and unrepresentative for this population? A. M = 53 and n = 16 B. M = 54 and n = 4 C. M = 56 and n = 4 D. M = 56 and n = 36

D. M = 56 and n = 36

Which of the following accurately describes the proportions of scores in the tails of a normal distribution? A. Proportions in both tails are negative. B. Proportions in the right-hand tail are negative, and proportions in the left-hand tail are positive. C. Proportions in the right-hand tail are positive, and proportions in the left-hand tail are negative. D. Proportions in both tails are positive (i.e., the value of proportion is always a positive number)

D. Proportions in both tails are positive (i.e., the value of proportion is always a positive number)

A normal distribution has a mean of µ = 60 with σ = 10. What score separates the highest 10% of the distribution from the rest of the scores? (Note: use the closest value to the top 10% listed in the Unit Normal table). A. X = 69.2 B. X = 100.8 C. X = 84.7 D. X = 72.8 E. none of the above

D. X = 72.8

Define the distribution of sample means and describe what is measured by the standard error of M.

The *distribution of sample means* is the *set of sample means* obtained from *all possible random samples* of a specific size (n) selected *from a particular population.* The *standard error of M* is the *standard deviation for the distribution of sample means*; it *measures the standard (i.e., average) difference between a sample mean M and the population mean µ.*

Explain what is indicated by the sign of a z-score and what by its numerical value

The sign of a z-score tells *whether the score is located above (+) or below (-) the mean*, and the *numerical value identifies the distance from the mean by measuring the number of standard deviations between the score and the mean.*

There is a sample of scores with M = 60 and s = 10. If this sample is standardized in order to create a new sample with M = 100 and s = 20, what would be the new value for each of the following scores from the original sample? Original sample scores (X): 55, 70, 60, 80

z= (X - M)/s Z1= (55 - 60)/10= -0.5 Z2= (70 - 60)/10= +1.0 Z3= (60 - 60)/10= 0 Z4= (80 - 60)/10= +2.0 X1= 100 + (-0.5)(20) = 90 X2= 100 + (+1.0)(20) = 120 X3= 100 + (0)(20) = 100 X4= 100 + (+2.0)(20) = 140