Introduction to Statistics
Exam Answer Key
Course Introduction
Introduction to Statistics provides students with the foundational concepts and methods necessary to collect, analyze, and interpret data. The course covers key topics such as descriptive statistics, probability theory, distributions, sampling, hypothesis testing, confidence intervals, and correlation. Emphasis is placed on understanding statistical reasoning, applying statistical techniques to real-world problems, and interpreting results through the use of statistical software. By the end of the course, students will be able to critically evaluate data and gain practical skills for research and professional applications.
Recommended Textbook
Answering Questions With Statistics 1st Edition by Robert F. Szafran
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Chapter 1: Introduction
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Sample Questions
Q1) What are some types of non-probability sampling and some types of probability sampling? Clearly indicate which are which.
Answer: Some types of non-probability sampling are convenience sampling, quota sampling, purposive sampling, and snowball sampling. Some types of probability sampling are simple random sampling, systematic random sampling, stratified random sampling, and multistage random sampling.
Q2) A researcher examines the effect of playing organized sports on a child's grades in school. Since grades are affected by many things besides involvement in organized sports, the researcher will also take into account the educational level and the socioeconomic status of the parents. What is the dependent variable?
A) child's grades
B) involvement in organized sports
C) parents' educational level
D) parents' socioeconomic status
Answer: A
Q3) What is the difference between reliability and validity?
Answer: Reliability refers to consistency of measurement whereas validity refers to the match between the operational and theoretical definitions.
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Chapter 2: Data Sets
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Sample Questions
Q1) Convert this number from scientific notation into normal notation: 7.89E+03
A) 7890
B) .00789
C) .00789
D) 7890
Answer: A
Q2) Which column in Variable View lets you attach labels to the codes for a variable's attributes?
A) Name
B) Label
C) Values
D) Role
Answer: C
Q3) What are two ways to get location-specific help in SPSS?
Answer: Use the help button on a dialog or position the cursor over a feature in the dialog and click the right mouse button to see if there is quick information available for that feature.
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Page 4
Chapter 3: Frequency Tables and Univariate Charts
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Sample Questions
Q1) What advantages do charts have over frequency tables? What advantages do frequency tables have over charts?
Answer: An advantage of charts is that they provide visual impact. Persons can more quickly grasp and remember things visually presented. An advantage of tables is that they usually provide more information and they provide it more precisely
Q2) Which column in a frequency table should you use to find the actual number of cases that gave a particular answer?
A) frequency
B) percent
C) valid percent
D) cumulative percent
Answer: A
Q3) Answer the question that follows this SPSS output:
The first bin in this histogram represents persons with _____ children up to but not including _____ children.
Answer: zero two
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Chapter 4: Central Tendency and Dispersion
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Sample Questions
Q1) A researcher takes a sample of three students from a playground and asks each of them what grade they are in. The students' answers are 3, 3, and 3. What is the variance for this data?
variance: __________
Q2) For interval/ratio data that is very positively skewed (that is, there are a few cases with extremely high values), the value of the mean will be _____ the value of the median.
A) greater than B) less than
C) the same as
Q3) When the scores on an interval/ratio variable are very negatively skewed, there are A) a few extremely low scores
B) a few extremely high scores
C) a few extremely low scores and a few extremely high scores
D) no extreme scores in either direction
Q4) You want to see the mode and percent distribution for a variable. Name one SPSS procedure that would give you this.
Q5) What is the difference between central tendency and dispersion?
Q6) Name five different univariate descriptive statistics.
Page 6
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Chapter 5: Creating New Variables
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Sample Questions
Q1) Why would an analyst want to know the value of Cronbach's alpha?
Q2) To limit an analysis to just a subset of the cases in a data set which meet a particular condition, you would use which SPSS procedure?
A) Compute
B) Recode
C) Select Cases
D) Split File
Q3) What are the two most common reasons for recoding a variable?
Q4) You are computing a new variable called CRIMEALL. It is the average of four variables already in your data set: CRIMESA, CRIMESB, CRIMESC, and CRIMESD. Write the numeric expression (formula) for a compute command that averages these four variables but only if all four of the CRIME variables being averaged have valid values.
Q5) You want to Compute a new variable that multiplies a person's hourly wage by their hours worked per week by their weeks worked per year. Write out the numeric expression that would accomplish this. (Variables: hourlyWage, hoursPerWeek, weeksPerYear)
Q6) When would you use Select Cases and when would you use Split File?
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Chapter 6: Comparing Group Means
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Sample Questions
Q1) Answer the questions that follow this SPSS output:
A) What is the mean years of schooling (EDUC) of blacks in the Midwest? __________
B) In the West, is there more variability in the years of schooling (EDUC) among whites or among blacks? (whites/blacks) _______________
C) Is there an interaction effect of REGION and RACE on EDUC? (yes/no) _______
D) State numerical evidence that justifies your conclusion about an interaction effect of REGION and RACE on EDUC.
Q2) A(n) _____ is when the size and/or direction of one independent variable's effect on the dependent variable varies depending on the value of one or more other independent variables.
A) asymmetry
B) correlation
C) interaction effect
D) main effect
Q3) What does layering independent variables do?
Q4) What kinds of questions can you answer using the Means procedure?
Q5) What is an interaction effect?
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Chapter 7: Crosstab Tables
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Sample Questions
Q1) You want to compare groups on a nominal variable (for example, preferred Presidential candidate of students at different colleges). Which SPSS procedure should you run?
A) Crosstabs
B) Display Data File Information
C) Frequencies
D) Means
Q2) In a clustered bar chart, why should the cases be clustered by categories of the independent variable?
Q3) In the following Crosstabs, what is the most common political orientation of males?
A) moderate
B) conservative
C) 38.3%
D) 44.9%
Q4) What kinds of questions can you answer using a crosstab table?
Q5) How can layering reveal if the relationship between the original two variables was spurious or not?
Q6) How can you use column percents to identify the median?
Page 9
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Chapter 8: Nominal and Ordinal Measures of Association
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Sample Questions
Q1) Which of the following is a proportional reduction in error (PRE) measure of association?
A) Cramer's V
B) gamma
C) lambda
D) tau-b
Q2) The value of Cramer's V is .65. This indicates what type of relationship?
A) strong and positive
B) strong
C) very strong and positive
D) very strong
Q3) What are the names of two nominal measures of association?
Q4) The height of a child and the age of a child are
A) inversely related
B) negatively related
C) positively related
Q5) What kinds of questions can you answer using a measure of association?
Q6) What is the difference between a symmetric and an asymmetric measure of association?
Q7) What are the names of two ordinal measures of association?
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Chapter 9: Pearsons Correlation and Bivariate Regression
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Sample Questions
Q1) Years of schooling (EDUC) is regressed on number of SIBLINGS. The resulting regression equation is EDUC = 16 1.00(SIBLINGS). Someone with three siblings would be predicted to get how many years of schooling?
A) 13
B) 15
C) 16
D) 17
Q2) If the value of the multiple correlation is .80, what is the value of the coefficient of determination? __________
Q3) Which of the following measures of association can range in value from 1.00 to 1.00?
A) Cramer's V
B) lambda
C) multiple correlation coefficient
D) Pearson's r
Q4) How does a scatterplot indicate the strength of the relationship between two variables?
Q5) If the coefficient of determination for a regression equation is .25, what is the value of the coefficient of alienation? __________
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Chapter 10: Multiple Regression
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Sample Questions
Q1) Answer the questions that follow this SPSS output:
If the three variables in the correlation matrix were all used as independent variables in a single multiple regression analysis, would there be a multicollinearity problem?
A) State yes or no. __________
B) Justify your answer by referring to one or more statistics in the matrix.
Q2) If the variables in this matrix were all used as independent variables in a regression equation, would there be a multicollinearity problem?
A) no
B) yes due to the correlation between ACT and SAT
C) yes due to the correlation between BIRTH and HSRank
D) yes due to the correlation between HSRank and SAT
Q3) What is a net effect?
Q4) For each of the following, indicate if it gives you information about the strength of a relationship and/or the direction of a relationship:
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Page 12
Chapter 11: Sampling Distributions and Normal Distributions
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Sample Questions
Q1) If a researcher wants to make a statement with a 95% level of confidence, the margin of error is the standard error multiplied by A) 1
B) 2
C) 3
D) 5
Q2) What does the central limit theorem say about sampling distributions?
Q3) A measure of dispersion for a sampling distribution is the
A) sampling frame
B) standard deviation
C) standard error
D) sampling interval
Q4) Which of the following statements is correct?
A) As the sample size increases, the standard error decreases.
B) Standard errors of sampling distributions can be calculated from the results of non-probability samples.
C) Both "a" and "b" are correct.
D) None of the above is correct.
Q5) Why do researchers prefer sampling distributions with small standard errors?
Q6) What are confidence intervals, confidence levels, and margins of error?
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Chapter 12: Hypothesis Testing and One-Sample T Tests
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Sample Questions
Q1) A researcher does a one-sample t test with 999 cases. How many degrees of freedom does the t test have? __________
Q2) What is Step 1 in hypothesis testing?
A) Check the significance level of your findings.
B) Convert ordinal and interval/ratio variables into nominal variables.
C) Select a 50% sample of your data for hypothesis testing.
D) State the research and the null hypothesis.
Q3) In order to reject the null hypothesis, the significance level must be _____ or less.
Q4) When is a one-sample t test used?
Q5) The results of a one-sample t test are reported as follows: t = 3.15, df = 430, p = .035.
Which of the following is correct?
A) There were 431 valid cases.
B) The null hypothesis was rejected.
C) The results were statistically significant.
D) All of the above are correct.
Q6) What is the difference between a two-tailed hypothesis test and a one-tailed hypothesis test?
Q7) What kinds of questions can you answer using a one-sample t test?
Page 14
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Chapter 13: Paired and Independent-Samples T Tests
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Sample Questions
Q1) Why are independent samples called that?
Q2) Answer the questions that follow this SPSS output:
Your research hypothesis is "In the population, the average number of hours spent using the Internet by full-time workers is greater than by part-time workers." (¯HEALTHSCORE06 ¯HEALTHSCORE05)
A) State the null hypothesis being tested.
B) Is this a one-tailed or two-tailed hypothesis?
C) Are your sample results consistent with the null hypothesis or the research hypothesis? (null / research)
D) What is the significance level? (If this step in hypothesis testing can be skipped, write the word "SKIP".)
E) What is your conclusion? (In other words, do you "reject" or "not reject" the null hypothesis based on these results?)
F) Are your results statistically significant? (yes / no)
Q3) Independent-samples t tests compare means for how many variables for how many groups of cases?
Q4) When does a researcher risk making a Type I error?
Q5) What kinds of questions can you answer using an independent-samples t test?
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Chapter 14: Analysis of Variance
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Sample Questions
Q1) You are doing a one-way ANOVA. What level of measurement is required on the two variables you are using? (Circle the letter of the correct answer.)
A) Both must be interval ratio.
B) Both can be any level.
C) The dependent variable can be any level, the factor variable must be interval/ratio.
D) The dependent variable must be interval/ratio, the factor variable can be any level.
Q2) Your research hypothesis is "In the population, first stays in the U.S. by unauthorized immigrants are on average longer than second stays in the U.S. by these same immigrants." What type of hypothesis test should be used?
A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA
Q3) Describe the interaction effect shown in this plot.
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Chapter 15: Chi-Square
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Sample Questions
Q1) What should you do next if chi-square is significant?
Q2) Variables included in a chi-square hypothesis test can have which levels of measurement?
Q3) A cell in a crosstab has an observed count of 50 and an expected count of 25. What is the value of the residual?
A) 25
B) 0.5
C) 2
D) 25
Q4) The text talks about the expected count in a cell of a crosstab. This is the expected count if
A) the row and column variables are independent
B) the row and column variables are significantly related
C) the row and column variables have identical means
D) the row and column variables have identical numbers of valid cases
Q5) What is the lowest level of measurement that can be used for the two variables in a chi-square analysis?
A) nominal
B) ordinal
C) interval/ratio
17
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Chapter 16: Hypothesis Testing With Measures of
Association and Regression
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Sample Questions
Q1) What kinds of questions can you answer using tests of significance for measures of association?
Q2) Which SPSS procedure would you use to answer the question "Is there a significant positive correlation between strength of attachment to a religion and amount given to charity?"
A) Bivariate Correlation
B) Chi-square
C) One-Sample T Test
D) One-way ANOVA
Q3) Which SPSS procedure would you use to answer the question "Is there a significant difference in the average amount given to charity by Americans, Germans, Japanese, and Swedes?"
A) Bivariate Correlation
B) Chi-square
C) Linear Regression
D) One-way ANOVA
Q4) What kinds of questions can you answer using tests of significance for regression coefficients?
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