psy 233 chapters 4-5
A z-score of z = +3.00 indicates a location that is a. far above the mean in the extreme right-hand tail of the distribution. b. the location depends on the mean and standard deviation for the distribution. c. slightly above the mean. d. near the center of the distribution.
a
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, the z-score would be _____. a. μ + 3σ b. +3.00 c. μ + 3 d. Cannot be determined from the information given.
b
A population has µ = 50. What value of σ would make X = 55 a more central, representative score in the population? a. σ = 1 b. σ = 5 c. σ = 10 d. σ = 20
d
College GPAs can range from 0.00 to 4.00. You collect GPAs from a sample of students and calculate a standard deviation of 6.13. This most likely implies that a. there is a great deal of variability in the GPAs of your sample. b. the distribution of GPAs is bimodal. c. the distribution of GPAs is symmetrical. d. you need to check your calculations.
d
A population with µ = 30, a score of X = 24 corresponds to z = -2.00. The standard deviation for the population is σ = 6. True False
false
A raw score with a value less than or equal to the mean will have a z-score that is less than or equal to 0. True False
true
After a researcher multiplies every score in a sample by 2, the standard deviation is found to be s = 10. The original sample had a standard deviation of s = 5. True False
true
For a particular sample size of n = 15, the largest distance (deviation) between a score and the mean is 9 points. The smallest distance between a score and the mean is 5 points. Therefore, the standard deviation will be _____. a. between 5 and 9 b. greater than 9 c. equal to 0 d. less than 5
a
The mean for any distribution corresponds to a z-score of _____. a. 0 b. Cannot be determined from the information given c. 1 d. N
a
The range is defined as a. the mathematical difference between the lowest and highest scores in a data set. b. average squared deviation of a score from the population mean. c. average squared deviation from the mean. d. the middle 50% of the scores in a set of data.
a
Which of the following is a strength of the range? a. It provides information about the sample from which the data were collected b. It accurately reflects the amount of variability in the entire distribution of scores c. It represents the variability in a set of data while lessening the influence of outliers d. It can be used in statistical analyses designed to test research hypotheses
a
Which of the following is an advantage of transforming raw scores into z-scores? a. None of these options are an advantage. b. All negative numbers are eliminated. c. The distribution is transformed into a normal shape. d. All scores are moved closer to the mean.
a
Which of the following is true for most distributions? a. Around 70% of the scores will be located within one standard deviation of the mean. b. Around 30% of the scores will be located within one standard deviation of the mean. c. Around 50% of the scores will be located within one standard deviation of the mean. d. Around 90% of the scores will be located within one standard deviation of the mean.
a
You would calculate the population standard deviation (σ) for a collected set of data when a. you have collected data from the entire population. b. you have collected data from a sample. c. your sample is larger than the population. d. you want to test hypotheses about populations.
a
Which of the following can be a negative number? a. The variance (σ² and s²) b. The mean (μ and M) c. The sum of squared deviations (SS) d. The standard deviation (σ and s)
b
You have a score of X = 65 on an exam. Which set of parameters would give you the best grade on the exam? a. µ = 70 and σ = 10 b. µ = 60 and σ = 5 c. µ = 70 and σ = 5 d. µ = 60 and σ = 10
b
Calculating the variance involves _____ deviations because _____. a. subtracting; deviations are always positive b. dividing; distributions are sometimes skewed or asymmetric c. squaring; the sum of unsquared deviations is equal to 0 d. multiplying; samples are smaller than populations
c
For a population with σ = 10, a score that is located 20 points above the mean would have a z-score of _____. a. -2.00 b. +20.00 c. +2.00 d. Cannot be determined without knowing the value of the mean
c
The _____ measures the _____ of a distribution of scores for a variable. a. mean; variability b. variance; symmetry c. standard deviation; variability d. range; symmetry
c
Variance may be defined as a. the most common or frequently occurring score in a distribution. b. the score that splits a distribution into two equal halves. t c. the average squared deviation of a score from the mean. d. the mathematical average.
c
Which of the following z-scores represents the location closest to the mean? a. -2.50 b. +1.25 c. -0.25 d. +0.75
c
Which of these is based on all of the scores in a set of data? a. median b. Range c. Variance d. Mode
c
If a population with μ = 122.51 and σ = 17.45 is transformed into z-scores, then the resulting distribution of z-scores will have a mean of _____ and a standard deviation of _____. a. 122.51; 17.45 b. 0; 17.45 c. 122.51; 1 d. 0; 1
d
Of the following z-score values, which one represents the most extreme location on the left-hand side of the distribution? a. +2.00 b. +1.00 c. -1.00 d. -2.00
d
The direct, unchanged scores that are the direct result of measurement are called a. z-scores. b. deviation scores. c. standardized scores. d. raw scores.
d
The smallest score in a population is X = 5 and the largest score is X = 10. Based on this information, you can conclude that the _____. a. standard deviation is greater than 8 b. mean is equal to 0 c. mean is greater than 10 d. standard deviation is smaller than 5
d
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 smaller than 15 b. When the population mean is much larger than 15 c. When the population standard deviation is much larger than 15 d. When the population standard deviation is much smaller than 15
d
Under what circumstances is a score that is located 5 points above the mean considered a central value that is 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.
d
What position in the distribution corresponds to a z-score of z = -1.50? a. Above the mean by 1.50 points b. Below the mean by 1.50 points c. Above the mean by a distance equal to 1.50 standard deviations d. Below the mean by a distance equal to 1.50 standard deviations
d
Which of the following is a weakness of the range? a. It takes into account all the scores of a distribution b. It lessens the influence of outliers by only taking into consideration 50% of the distribution c. It is difficult to compute d. It may not accurately reflect the amount of variability in the entire distribution
d
Which of the following represents the deviation score? a. μ b. s² c. X d. (X - μ)
d
Which of these is based on all of the scores in a set of data? a. Range b. Median c. Mode d. Standard deviation
d
You calculate a value of -1.87 for the variance for a set of data. This necessarily implies that a. most of the scores are less than the mean. b. there are outliers in the data. c. the distribution of scores in negatively skewed. d. you need to check your calculations.
d
After a researcher adds 5 points to every score in a sample, the standard deviation is found to be s = 10. The original sample had a standard deviation of s = 5. True False
false
Any individual with a negative z-score has a raw score greater than the mean. True False
false
If you have a score of X = 76 on an exam with µ = 70, you should expect a better grade if σ = 10 than if σ = 5 True False
false
In a distribution with s = 20, a score that is above the mean by 10 points will have a z-score of z = -0.50. True False
false
In a population with a mean of µ = 40 and a standard deviation of σ = 8, a score of X = 46 would be an extreme value, far out in the tail of the distribution. True False
false
Multiplying every score in a sample by 3 will not change the value of the standard deviation. True False
false
Because all z-score distributions have the same mean and standard deviation, the z-score distribution is called a standardized distribution. True False
true
For a population with a mean of µ = 72, any score greater than 72 will have a positive z-score. True False
true
For a population, a deviation score is computed as X - µ. True False
true
For a sample with M = 20 and s = 1, a score of X = 17 would be considered an extremely low score. True False
true
For any distribution of scores, the location identified by z = +1.00 and the location identified by z = -1.00 are exactly the same distance from the mean. True False
true
If two individuals in the same population have identical X values, they also will have identical z-scores. True False
true
It is easier to see the mean difference between two samples if the sample variances are small. True False
true
Standardized scores are "simple" values for the mean and standard deviation that do not change any individual's location within the distribution. True False
true
The process of transforming every X value in a distribution into a corresponding z-score to create a distribution of z-scores is called a z-score transformation. True False
true
The range and the standard deviation are both measures of spread. True False
true
The range is usually considered to be a relatively crude measure of variability. True False
true