Quiz 2 (chapters 4-5)

For a population with mean mu=80 and standard deviation sigma=12, what is the z-score corresponding to X=71?

-0.75

For a population with mean mu=80 and standard deviation sigma=12, what is the z-score corresponding to X=92?

1.0

For a population with mean mu=80 and standard deviation sigma=10, what is the z-score corresponding to X=95?

1.5

What is the third quartile of the following set of nine scores? (Use the method in which you include the median in both "halves" of the dataset). 1, 4, 5, 6, 8, 11, 14, 17, 22

14

A population of N=5 scores has a sum of scores (sigma-X) = 20 and a sum of squared scores (sigma(X^2)) = 100. For this population, what is the value of SS? (Hint: use the computational formula).

20 (Specifically, SS = 100 - (20^2)/5 using the computational formula for SS, which evaluates to 100-80 or 20.)

A population of N=10 scores has a mean of mu=50 and a standard deviation of sigma=5. What is the population variance?

25 (the population variance sigma^2 is 25 (the square of the population standard deviation sigma))

A very bright student is described as having an IQ that is three standard deviations above the mean. If this student's IQ is reported as a z-score (rather than as an IQ score), the z-score would be ________.

3.0

A sample of n=5 scores produces SS=20. The variance for this sample is ________.

5 ( the sample variance s^2 = SS/(n-1) = 20/4 = 5)

A sample has M=72 and s=4. In this sample, what is the X value (raw score) corresponding to z = -2.00?

64 (Specifically, a value z = -2.00 corresponds to two standard deviations below the mean, so 72 - 2(4) = 64.)

What is the interquartile range of the following set of nine scores? 1, 4, 5, 6, 8, 11, 14, 17, 22. (Use the method in which you include the median in both "halves" of the dataset).

9 (Specifically, Q3 = 14, Q1 = 5, and the IQR = Q3-Q1 = 14-5 = 9.)

A sample has SS=20 and s2=4. How many scores are in the sample? A. 6 B. 4 C. cannot be determined without additional information D. 5

A. 6 (there are 6 scores in the sample. The sample variance s2 = SS/(n-1), so (n-1) must be 5, hence n = 6.)

A population of scores has a mean of mu=50 and a standard deviation of sigma=10. If every score in the population is multiplied by 2, then the new mean and standard deviation would be _________. A. mu=100 and sigma=20 B. mu=100 and sigma=10 C. mu=50 and sigma=10 D. mu=50 and sigma=20

A. mu=100 and sigma=20 (Both the mean and standard deviation are multiplied by the same factor that is applied to each of the scores.)

A population of scores has a mean of mu=50 and a standard deviation of sigma=10. If five points are added to every score in the population, then the new mean and standard deviation would be _________. A. mu=55 and sigma=10 B. mu=55 and sigma=15 C. mu=50 and sigma=10 D. mu=50 and sigma=15

A. mu=55 and sigma=10 (The mean increases along with the addition to each value, whereas the standard deviation is unchanged)

For a particular sample, the largest deviation between a score and the mean is 11 points, and the smallest distance between a score and the mean is 4 points. Therefore, the standard deviation ____________. A. will be between 4 and 11 B. it is impossible to say anything about the value of the standard deviation C. will be greater than 11 D. will be less than 4

A. will be between 4 and 11

Which set of scores has the smallest standard deviation? (you should not need to explicitly do the math here). A. 27, 105, 10, 80 B. 145, 143, 145, 147 C. 5, 11, 42, 22 D. 11, 17, 31, 53

B. 145, 143, 145, 147 (has the smallest standard deviation, because the variability among these four scores is much less than the variability within any of the other sets of scores.)

A distribution with mean mu=55 and standard deviation sigma=6 is being standardized so that the new mean and standard deviation will be mu=50 and sigma=10. When the distribution is standardized, what value will be obtained for a score of X=52 from the original distribution? A. 58 B. 45 C. 47 D. 52

B. 45 (Correct; a score of X=52 will correspond to a standardized score of 45. Specifically, X=52 corresponds to z=-0.50, which corresponds to one half of a standard deviation below the mean, which corresponds in the new standardized distribution to 45.)

A sample of n=10 scores is selected from a population. The sample mean is M=24, and the sample standard deviation is s=4. What are the degrees of freedom? A. the degrees of freedom cannot be determined from the information provided B. 9 C. 10 D. 6

B. 9 (df = n -1)

For the past 20 years, the high temperature on April 15th has averaged mu = 62 degrees with a standard deviation of sigma = 12. Last year, the high temperature was 68 degrees. Based on this information, which of the following best describes last year's temperature on April 15th? A. above average, but it is impossible to describe how much above average B. far above average C. a little above average D. there is not enough information to compare last year's temperature with the average

C. a little above average (last year's temperature on April 15th was a little above average (z = +0.5). To be considered far above average, as a rule of thumb, z should be at least +2 standard deviations, corresponding to a temperature of over 86 degrees in this example.)

Which of the following symbols identifies the population variance? ("Sigma" below refers to the lowercase Greek letter sigma, not the uppercase sigma that means "sum of"). A. s^2 B. sigma C. sigma2 D. s

C. sigma^2 (sigma^2 denotes population variance. The term s^2 denotes sample variance, and the non-squared terms denote standard deviations.)

The interquartile range of a sample is __________. A. the distance from the mean to the third quartile B. the distance from the median to the first (or third) quartile C. the distance between the first and third quartiles D. the distance between the first and second quartiles

C. the distance between the first and third quartiles

The third quartile (Q3) of a sample of scores is __________. A. equal to the median plus the value of Q1 B. the point where 25% of the scores are less than Q3 and 75% of the scores are greater than Q3 C. the point where 75% of the scores are less than Q3 and 25% of the scores are greater than Q3 D. equal to the median plus the interquartile range

C. the point where 75% of the scores are less than Q3 and 25% of the scores are greater than Q3

A population distribution has a mean of mu=80 and a standard deviation of sigma=6. In this distribution, a z-score of z = +2.00 identifies a location that is _______________. A. twelve points below the mean B. two points above the mean C. twelve points above the mean D. two points below the mean

C. twelve points above the mean (z = +2.00 identifies a location that is twelve points above the mean -- that is, a score of X=92, or two standard deviations above the mean.)

For a distribution of scores, which of the following z-score values represents the location closest to the mean? A. z = +1.00 B. z = -0.75 C. z = +0.50 D. it cannot be determined from the information given

C. z = +0.50

The symbol SS stands for the _____. A. sum of squared scores B. sum of the deviations, squared C. sum of scores, squared D. sum of squared deviations

D. sum of squared deviations (sum of squares for short)

Under what circumstances would a score that is 15 points above the mean be considered an extreme score? A. when the population standard deviation is much larger than 15 B. when the population mean 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 smaller than 15 (because it would increase the z-score corresponding to that raw score of 15)