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Various statistical concepts including scales of measurement, mean, median, mode, variance, standard deviation, z-scores, and normal distributions. It also includes examples and exercises related to determining class standing, computing sums of squared deviations, and identifying the shape of distributions. Useful for students in statistics, mathematics, or education courses.
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Although a research study is typically conducted with a relatively small group of participants known as a _____, most researchers hope to generalize their results to a much larger group known as a _______. A. population; sample B. sample; population C. statistic; sample D. parameter; population - B A researcher interested in vocabulary development obtains a sample of 3-yr-old children to participate in a research study. The average score for the group of 20 is an example of a parameter. A. true B. false - B values of data measured on this scale can be rank ordered. In addition, the differences between 2 adjacent ranks are equal - Interval Scale values of data measured on this scale can be rank ordered - Ordinal Scale
values of data measured on this scale can be rank ordered and have meaningful differences between scale points. For this scale, there is also an absolute zero point. - Ratio Scale the values of data measured on this scale cannot be rank ordered - Nominal Scale determining a person's reaction time (in milliseconds) would involve measurement on a(n) ____ scale of measurement. A. ordinal B. interval C. ratio D. nominal - C determining the class standing (1st, 2nd, and so on) for the graduating seniors at a high school would involve measurement on a(n) ____ scale of measurement. A. nominal B. ratio C. interval D. ordinal - D
What is the value of Σ(X + 1) for the following scores? Scores: 2, 4, 7 A. 13 B. 16 C. 10 D. 11 - B A set of three scores consists of the values 6, 3, and 2. Σ2(X - 3) = _______ - 4 Σ(2X)^2 = _______ - 196
What is the mean for the following sample of scores? Scores: 1, 4, 5, 10 A. 5 B. 20 C. 10 D. 4 - 5 A population with a mean of M = 6 has ΣX = 42. How many scores are in the population? A. N = 6/42 = 1/ B. N = 7 C. N = 252 D. it cannot be determined from the information given. - B After every score in a sample is multiplied by 3, the mean is calculated and found to be M = 21. What was the mean for the original score? A. it cannot be determined from the information given. B. 21
What is the median for the following set of scores? Scores: 1, 2, 6, 11, 17 A. 8 B. 4 C. 6 D. 8.5 - C Which of the following statements cannot be true for a distribution of scores? A. all of these options are false statements. B. 60% of the scores are above the median. C. 60% of the scores are above the mean D. 60% of the scores are above the mode - B A researcher measures eye color for a sample of n = 50 people. Which measure of central tendency would be appropriate to summarize the measurements? A. any of these measures could be used. B. median
C. mean D. mode - D A sample consists of n = 16. How many of the scores are used to calculate the range? A. 8 B. 4 C. 2 D. all 16 - C What is the value of SS for the following sample? Sample: 2, 3, 4, 7 A. 14 B. 28 C. 72 D. 14/3 = 2.67 - A A population has SS = 100 and σ^2 = 4. How many scores are in the population?
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 = 10; σ^2 = 10 B. s^2 = 9; σ^2 = 9 C. s^2 = 9; σ^2 = 10 D. s^2 = 10; σ^2 = 9 - D The sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores. What is the variance for this sample? A. 4 B. 5 C. 100 D. 80 - B A population of scores has μ = 50 and σ = 5. If every score in the population is multiplied by 3, then what are the new values for the mean and standard deviation?
A. μ = 50; σ = 5 B. μ = 50; σ = 15 C. μ = 150; σ = 15 D. μ = 150; σ = 5 - C What is the variance for the following population of scores? Scores: 5, 2, 5, 4 A. 1. B. 1. C. 2 D. 6 - B Which set of scores has the smallest standard deviation? A. 145, 143, 145, 147 B. 27, 105, 10, 80 C. 11, 17, 31, 53 D. 5, 11, 42, 22 -
For the following distribution of quiz scores, if a score of X = 3 or higher is needed for a passing grade, how many individuals passed? X: 5 4 3 2 1 f: 6 5 5 3 2 A. 11 B. 16 C. cannot be determined D. 3 - B For the following frequency distribution of exam scores, what is the lowest score on the exam? X: 90-94 85-89 80-84 75-79 70- f: 3 4 5 2 1 A. x = 70 B. x = 74 C. cannot be determined D. x = 90 - C
For the following distribution, what is the width of each class interval? X: 20-24 15-19 10-14 5- f: 2 5 4 1 A. 10 B. 5 C. 4. D. 4 - B What is the mean for the population of scores shown in the frequency distribution table? X: 5 4 3 2 1 f: 1 2 3 4 2 A. 15/5 = 3 B. 32/5 = 6. C. 32/12 = 2. D. 15/12 = 1/25 - C
C. nominal or ordinal D. interval or ratio - C If a set of exam scores forms a symmetrical distribution, what can you conclude about the students' scores? A. it is not possible to draw any conclusions about the students' scores B. most of the students had relatively high scores C. about 50% of the students had high scores and the rest had low scores D. most of the students had relatively low scores - C The students in a psychology class seemed to think that the midterm exam was very easy. If they are correct, what is the most likely shape for the distribution of exam scores? A. positively skewed B. negatively skewed C. normal D. symmetrical - B
What is the shape of the distribution for the following set of data? Scores: 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6 A. symmetrical B. cumulative C. negatively skewed D. positively skewed - C What percentage of the normal distribution is below the mode? A. 50% B. 25% C. 85% D. unable to determine from the info above - A Josh is a very good singer. In fact, he participated in a study recently for the music department and he was told that he was one standard deviation above the mean in holding a tune. Based on the 1-2-3 Rule, what is Josh's percentile rank? - 84%
A. z = -2. B. z = -1. C. z = +1. D. z = +0.50 - D For a population with a standard deviation of σ = 6, what is the z-score corresponding to a score that is 12 points above the mean? A. z = 2 B. z = 6 C. z = 12 D. z = 1 - A For a population with μ = 40 and σ = 8, what is the z-score corresponding to X = 46? A. +0. B. +0. C. +1.
A population distribution has σ = 6. What position in this distribution is identified by a z-score of z = +2.00? A. two points above the mean B. two points below the mean C. twelve points below the mean D. twelve points above the mean - D On an exam with μ = 52, you have a score of X = 44. Which value for the standard deviation would give you the highest position in the class distribution? A. σ = 8 B. σ = 4 C. It cannot be determined from the information given D. σ = 2 - A For a sample with M = 50 and s = 12, what is the X value corresponding to z = -0.25?