Educational Statistics
Final Test Solutions
Course Introduction
Educational Statistics introduces students to the fundamental concepts and methods used to collect, analyze, and interpret data in educational settings. The course covers key topics such as descriptive and inferential statistics, probability, sampling techniques, hypothesis testing, correlation, regression, and the use of statistical software. Emphasis is placed on understanding how statistical reasoning can be applied to evaluate educational research, assess student performance, and inform decision-making processes within schools and educational organizations. Through practical exercises and real-world examples, students gain the skills necessary to critically analyze data and draw meaningful conclusions to support educational practice and policy.
Recommended Textbook
The Essentials of Statistics A Tool for Social Research 2nd Edition by Joseph F. Healey
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15 Chapters
716 Verified Questions
716 Flashcards
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Chapter 1: Introduction
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Sample Questions
Q1) In terms of the Wheel of Science,a hypothesis is derived from ____ and leads to ____.
A)statistics;observation
B)theory;generalizations
C)observation;generalizations
D)theory;observation
Answer: D
Q2) A researcher has numbered all 50 states from 1 to 50 and has calculated a mean of 17.43 for the variable "state of birth."
A)Since the variable is nominal,the mean makes no sense.
B)Since the variable is ordinal,we should treat the value of the mean with great caution.
C)The variable is interval-ratio and the mean is an appropriate and useful statistic in this case.
D)Since this variable is discrete,the mean should not be computeD.
Answer: A
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3
Chapter 2: Basic Descriptive Statistics: Percentages Ratios
and Rates Frequency Distributions
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Sample Questions
Q1) A frequency distribution should reflect a balance of A)detail and conciseness.
B)time and money.
C)questions and answers.
D)elegance and symmetry.
Answer: A
Q2) Proportions and percentages,ratios and rates are all ways of expressing
A)concise distributions of a variable.
B)data without leaving out any details.
C)relative frequencies.
D)raw frequencies.
Answer: C
Q3) The purpose of univariate descriptive statistics is to
A)summarize relationships between many variables.
B)display the essential meaning of variables measured at the interval-ratio level.
C)combine nominal and discrete variables.
D)summarize a single variable.
Answer: D
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Chapter 3: Charts and Graphs
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Sample Questions
Q1) Which of the following is a characteristic of graphs and charts as compared to frequency distributions?
A)Graphs and charts always present less information.
B)Graphs and charts always present more information.
C)Graphs and charts can be more dramatic visually.
D)Graphs and charts are harder for most people to appreciate.
Answer: C
Q2) Histograms and line charts or frequency polygons are used with data measured at A)the nominal level.
B)the ordinal level.
C)the interval-ratio level.
D)any level.
Answer: C
Q3) For a single variable at the interval-ratio level,an appropriate graph would be A)a pie chart.
B)a histogram.
C)a bivariate table.
D)none of these.Graphs are never used for interval-ratio level variables.
Answer: B
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Page 5
Chapter 4: Measures of Central Tendency
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Sample Questions
Q1) If the scores on a variable are 11,14,18,20,and 25,the median is A)3.
B)16.
C)18.
D)19.
Q2) A distribution of income for a sample of 45 people that included the presidents of the 5 largest corporations in the United States and 40 assembly line workers would be A)unskewed.
B)negatively skewed.
C)positively skewed.
D)symmetrical.
Q3) If the scores of an even number of cases are arranged from high to low,the median is
A)the middle score.
B)the average of the two middle scores.
C)the average of the highest and lowest scores.
D)the same as the mode.
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Chapter 5: Measures of Dispersion
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Sample Questions
Q1) The expression \(\Sigma\left(X_{i}-\bar{X}\right)\)
Instructs us to
A)sum the scores
B)sum the scores and then subtract the mean
C)subtract every "ith" score from the mean
D)subtract the mean from each score and add up the deviations
Q2) Since computation of the standard deviation requires addition,division,and other mathematical operations,it should be used for A)interval-ratio level variables.
B)variables at any level of measurement.
C)nominal level variables only.
D)ordinal variables only.
Q3) When you subtract the value of the mean from each score in a distribution and then add the results,the sum will be A)0.
B)the standard deviation.
C)the variance.
D)a positive number.
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Chapter 6: The Normal Curve
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Sample Questions
Q1) A defining characteristic of the normal curve is that it is A)theoretical.
B)positively skewed.
C)negatively skewed.
D)perfectly nonsymmetrical.
Q2) The area between the mean and a Z score of +1.50 is 43.32%.This score is less than ____ of the scores in the distribution.
A)43.32%
B)6.68%
C)3.32%
D)93.32%
Q3) Converting scores into Z scores standardizes the original distribution to units of the A)median.
B)standard deviation.
C)mean.
D)percentage.
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Chapter 7: Introduction in Inferential Statistics, the
Sampling Distribution, and Estimation
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Sample Questions
Q1) Polls tracking the presidential election of 2004 showed that
A)Bush lead by a clear margin from start to finish.
B)Kerry lead by a clear margin until just a week before election day.
C)the race was "too close to call" during much of the campaign.
D)voter turnout would be extraordinarily high.
Q2) In estimation procedures,the Z score that corresponds to an alpha of .05 is
A)\(\pm\)1.96.
B)\(\pm\)2.58.
C)\(\pm\)3.78.
D)\(\pm\)9.78.
Q3) Compared to probability samples,non-probability samples
A)are usually cheaper to assemble.
B)are always much larger.
C)are usually more expensive to assemble.
D)allow for generalizations to populations.
Q4) In estimation procedures,____ are estimated based on the value of ____.
A)statistics;parameters
B)parameters;statistics
C)values;frequencies
D)sample;populations
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Chapter 8: Hypothesis Testing I: the One-Sample Case
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Sample Questions
Q1) The research hypothesis (H<sub>1</sub>)typically states what the researcher expects to find and A)contradicts the null hypothesis.
B)verifies on the null hypothesis.
C)modifies the null hypothesis.
D)is unrelated to the null hypothesis.
Q2) The probability of Type I error is A).01.
B).05.
C)the alpha level.
D)beta.
Q3) An alpha of 0.01 means that a decision to ____ the null hypothesis has a ____ in 100 chance of being incorrect
A)accept;1
B)fail to reject;1
C)reject;1
D)reject;100
Q4) Cite an example of a research situation in which a one-tailed test of significance would be appropriate.
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Chapter 9: Hypothesis Testing II: the Two-Sample Case
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Sample Questions
Q1) When testing for the significance of the difference between two samples,which is the proper assumption for step 1?
A)random sampling
B)ordinal level of measurement
C)degrees of freedom are zero
D)samples are independent as well as random
Q2) When solving the formula for finding Z(obtained)with sample proportions in the two-sample case,we must first estimate
A)the standard deviation of the population.
B)the population proportion.
C)the ratio of the sample proportions.
D)the critical region.
Q3) When random samples are drawn so that the selection of a case for one sample has no effect on the selection of cases for another sample,the samples are
A)dependent.
B)independent.
C)simple.
D)systematic.
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Chapter 10: Hypothesis Testing III: the Analysis of Variance
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Sample Questions
Q1) If we fail to reject the null hypothesis in a test using analysis of variance,we are concluding that
A)the populations from which our samples come are the same.
B)the samples are dependent.
C)the population variances are the different.
D)the sample means are different.
Q2) If our F (obtained)exceeds the F (critical),we
A)reject the null.
B)accept the null.
C)must recompute since this is mathematically impossible.
D)reject the research hypothesis.
Q3) A researcher is analyzing regional differences in family size.She has information on number of children for samples of families from four regions.Which of the following would be an appropriate statistical test?
A)t test for matched samples
B)t test for difference in means
C)ANOVA
D)Actually,none of these would work in this situation
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Chapter 11: Hypothesis Testing Iv: Chi Square
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Sample Questions
Q1) Chi square is used to test relationships for their A)empirical importance.
B)logical importance.
C)statistical significance.
D)theoretical importance.
Q2) In the Chi square test for independence,the research hypothesis is A)always one-tailed.
B)the variables are dependent.
C)the variables are independent.
D)expected frequencies are greater than observed frequencies.
Q3) A Chi square test has been conducted to assess the relationship between marital status and church attendance.The obtained Chi square is 23.45 and the critical Chi square is 9.488.What may be concluded?
A)reject the null hypothesis,church attendance and marital status are dependent
B)reject the null hypothesis,church attendance and marital status are independent
C)fail to reject the null hypothesis,church attendance and marital status are dependent
D)fail to reject the null hypothesis,church attendance and marital status are independent
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Chapter 12: Introduction to Bivariate Association and
Measures of Association for Variables Measured at the
Nominal Level
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Sample Questions
Q1) Proportional reduction in error (PRE)measures of association are based on the logic of A)percentages.
B)inference.
C)prediction.
D)zero errors.
Q2) For variables measured at the ordinal and interval-ratio levels,measures of association will have a lower limit of ____ and an upper limit of ____.
A)0;100
B)0;\(\pm\)1
C)0;1
D)1;0
Q3) In the case of a perfect association,predictions from one variable to another can be made
A)only if variables are measured at the nominal level.
B)when at least one variable is ordinal.
C)without error.
D)only if the relationship is positive.
Page 14
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Chapter 13: Association Between Variables Measured at the
Ordinal Level
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Sample Questions
Q1) A researcher tested the relationship between occupational prestige and level of approval of a proposal to ban handguns in the state and found a gamma of -0.17.This relationship is
A)weak and negative.
B)strong and negative.
C)weakly moderate.
D)positive and weak.
Q2) For a relationship involving education and library use,gamma was +0.37.This relationship is
A)weak and positive.
B)strong and negative.
C)moderate and positive.
D)positive and weak.
Q3) In the formula for gamma,N<sub>s</sub> represents the number of pairs of cases
A)in all similar cells.
B)ranked the same on both variables.
C)in all cells.
D)that have the same score.
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Chapter 14: Association Between Variables Measured at the
Interval-Ratio Level
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Sample Questions
Q1) If a line is drawn through the conditional means of Y,the line will A)always be perfectly linear.
B)rarely be a perfectly straight line.
C)always be parallel to the horizontal axis.
D)always be parallel to the vertical axis.
Q2) For interval-ratio level variables,the scattergram is analogous to ____ for nominal and ordinal level variables.
A)chi square
B)percentages
C)row marginals
D)bivariate tables
Q3) If the regression line showing the effect of education on income has a slope of 1000, A)the variables are not related.
B)every year of education increases income by 1000.
C)every change in education increases income.
D)the Y intercept would be 1.00.
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Chapter 15: Partial Correlation and Multiple Regression and Correlation
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Sample Questions
Q1) The partial correlation coefficient will reveal an interactive relationship between three variables when
A)the partial correlation coefficients drops to zero.
B)the partial is greater in value than the zero-order correlation coefficient.
C)the partial correlation coefficient is negative.
D)none of these.Partial correlation will not detect interaction.
Q2) If a = 1,b<sub>1</sub> = 10,b<sub>2</sub> = 10,X<sub>1</sub>= 2,and X<sub>2</sub>
= 3,what would the predicted Y score be?
A)51
B)26
C)5
D)0
Q3) Partial and multiple correlation require data which are
A)nominal and continuous.
B)ordinal and discrete.
C)inferential and bivariate.
D)interval-ratio.
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Page 17