Statistics for Social Sciences
Midterm Exam
Course Introduction
Statistics for Social Sciences is an introductory course designed to familiarize students with fundamental statistical concepts and techniques as they apply to social research. The course covers topics such as descriptive and inferential statistics, probability distributions, hypothesis testing, correlation, regression analysis, and the interpretation of data within a social context. Emphasis is placed on understanding how to critically evaluate statistical information, design experiments and surveys, and use statistical software to analyze real-world data commonly encountered in the fields of sociology, psychology, political science, and related disciplines. By the end of the course, students will be equipped with essential quantitative skills to conduct and assess empirical research in the social sciences.
Recommended Textbook
Statistical Techniques in Business and Economics 17th Edition by Douglas Lind
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Page 2
Chapter 1: What Is Statistics
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Sample Questions
Q1) Categorizing voters as Democrats,Republicans,and Independents is an example of interval level measurement.
A)True
B)False
Answer: False
Q2) What level of measurement is a person's "favorite sport"?
A)Ratio
B)Ordinal
C)Interval
D)Nominal
Answer: D
Q3) When statisticians analyze sample data in order to draw conclusions about the characteristics of a population,this is referred to as
A)descriptive statistics.
B)statistical inference.
C)data analysis.
D)data summarization.
Answer: B
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Chapter 2: Describing Data: Frequency Tables, Frequency
Distributions, and Graphic Presentation
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Sample Questions
Q1) The monthly salaries of a sample of 100 employees were rounded to the nearest $10. They ranged from a low of $1,040 to a high of $1,720. If we want to condense the data into seven classes,what is the most convenient class interval?
A)$50
B)$100
C)$150
D)$200
Answer: B
Q2) In a bar chart,the horizontal axis is usually labeled with the values of a qualitative variable.
A)True
B)False
Answer: True
Q3) A class interval can be determined by subtracting the lower limit of a class from the lower limit of the next higher class.
A)True
B)False Answer: True
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Chapter 3: Describing Data: Numerical Measures
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Sample Questions
Q1) On a finance exam,15 accounting majors had an average grade of 90. On the same exam,7 marketing majors averaged 85,and 10 finance majors averaged 93. What is the weighted mean for all 32 students taking the exam?
A)89.84
B)89.33
C)89.48
D)10.67
Answer: A
Q2) When computing the arithmetic mean,the smallest value in the data set
A)can never be negative.
B)can never be zero.
C)can never be less than the mean.
D)can be any value.
Answer: D
Q3) Which one of the following is referred to as the population mean?
A)µ
B)s
C)
D) Answer: A
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Chapter 4: Describing Data: Displaying and Exploring Data
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Sample Questions
Q1) A dot plot can be used to show ________.
A)the mean,median,and mode
B)the general shape of a distribution for a nominal qualitative variable
C)the distribution for a quantitative variable
D)the interquartile range
Q2) In a distribution,the second quartile corresponds with the ________.
A)mean
B)median
C)mode
D)variance
Q3) A dot plot is best applied for a data set with ________.
A)1,000 observations
B)50 observations
C)more than one variable
D)one mode
Q4) The "box" in a box plot shows the interquartile range.
A)True
B)False
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6
Chapter 5: A Survey of Probability Concepts
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Sample Questions
Q1) A survey of top executives revealed that 35% of them regularly read Time magazine,20% read Newsweek,and 40% read U.S. News & World Report. A total of 10% read both Time and U.S. News & World Report. What is the probability that a particular top executive reads either Time or U.S. News & World Report regularly?
A)0.85
B)0.06
C)1.00
D)0.65
Q2) If P(A) = 0.62, P(B) = 0.47, and P(A or B) = 0.88, then P(A and B) = ________.
A) 0.2914
B) 1.9700
C) 0.6700
D) 0.2100
Q3) Bayes' theorem is used to calculate a subjective probability.
A)True
B)False
Q4) If two events are mutually exclusive,then P(A and B)= P(A)× P(B).
A)True
B)False
Page 7
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Chapter 6: Discrete Probability Distributions
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Sample Questions
Q1) The probability of a particular outcome must always be between 0.0 and 1.0 inclusive.
A)True
B)False
Q2) Which of the following is correct about a probability distribution?
A)The sum of all possible outcomes must equal 1.0.
B)The outcomes must be mutually exclusive.
C)The probability of each outcome must be between 0.0 and 1.0 inclusive.
D)All of these answers are correct.
Q3) An insurance agent has appointments with four prospective clients tomorrow. From past experience the agent knows that the probability of making a sale on any appointment is one out of five. Using the rules of probability,what is the likelihood that the agent will sell a policy to three of the four prospective clients?
A)0.250
B)0.500
C)0.410
D)0.026
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8
Chapter 7: Continuous Probability Distributions
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Sample Questions
Q1) The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is less than 135 minutes?
A)1.00
B)0.50
C)0.25
D)0.00
Q2) The average starting salary of individuals with a master's degree in statistics is normally distributed with a mean of $48,000 and a standard deviation of $6,000. What is the probability that a randomly selected individual with a master's in statistics will get a starting salary of at least $55,000?
A)0.121
B)0.891
C)0.379
D)0.098
Q3) The normal distribution can be used to approximate a binomial distribution when n is less than 5.
A)True
B)False
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Chapter 8: Sampling Methods and the Central Limit
Theorem
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Sample Questions
Q1) The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. Based on a large number of observations,the distribution of trout weights is normally distributed with a mean of 402.7 grams and a standard deviation of 8.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?
A)0.3782
B)0.0222
C)1.0
D)0.5
Q2) Suppose we select every fifth invoice in a file. What type of sampling is this?
A)Random
B)Cluster
C)Stratified
D)Systematic
Q3) If the size of a sample equals the size of the population,we would not expect any error in estimating the population parameter.
A)True
B)False
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Chapter 9: Estimation and Confidence Intervals
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Sample Questions
Q1) The population variation has little or no effect in determining the size of a sample selected from the population.
A)True
B)False
Q2) A survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98,with a standard error of $0.10. What is the 98% confidence interval to estimate the true cost of a gallon of milk?
A)$2.73 to $3.23
B)$2.85 to $3.11
C)$2.94 to $3.02
D)$2.95 to $3.01
Q3) When we use a confidence interval to reach a conclusion about the population mean,we are applying a type of reasoning or logic called ________.
A)descriptive statistics
B)the normal distribution
C)statistical inference
D)graphics
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11
Chapter 10: One-Sample Tests of Hypothesis
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Sample Questions
Q1) Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to increase daily sales. To determine the effectiveness of the advertising campaign,a sample of 49 days of sales were taken. They found that the average daily sales were $6,300 per day. From past history,the restaurant knew that its population standard deviation is about $1,000. If the level of significance is 0.025,have sales increased as a result of the advertising campaign?
A)Fail to reject the null hypothesis.
B)Reject the null hypothesis and conclude the mean is higher than $6,000 per day.
C)Reject the null hypothesis and conclude the mean is lower than $6,000 per day.
D)Reject the null hypothesis and conclude that the mean is equal to $6,000 per day.
Q2) For a one-tailed hypothesis test,the critical z-value of the test statistic is 2.33. Which of the following is true about the hypothesis test?
A) = 0.05 for a lower-tailed test
B) = 0.01 for a lower-tailed test
C) = 0.05 for an upper-tailed test
D) = 0.01 for an upper-tailed test
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12
Chapter 11: Two-Sample Tests of Hypothesis
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Sample Questions
Q1) We test for a hypothesized difference between two population means: H<sub>0</sub>: <sub>1</sub> = <sub>2</sub>. The population standard deviations are unknown but assumed equal. The number of observations in the first sample is 15 and 12 in the second sample. How many degrees of freedom are associated with the critical value?
A)24
B)25
C)26
D)27
Q2) When testing the hypothesized equality of two population means,the implied null hypothesis is ________.
A)H<sub>0</sub>: µ<sub>1</sub> = 0
B)H<sub>0</sub>: µ<sub>1</sub> µ<sub>2 </sub>= 0
C)H<sub>0</sub>: µ<sub>2</sub> = 0
D)H<sub>0</sub>: µ<sub>1</sub> µ<sub>2</sub> 0
Q3) A statistics professor wants to compare grades in two different classes of the same course. This is an example of a paired sample.
A)True
B)False
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Page 13
Chapter 12: Analysis of Variance
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Sample Questions
Q1) An electronics company wants to compare the quality of their cell phones to the cell phones from three competitors. They sample 10 phones from each company and count the number of defects for each phone. If ANOVA was used to compare the average number of defects,then the treatments would be defined as ________.
A)the number of cell phones sampled
B)the average number of defects
C)the total number of phones
D)the four companies
Q2) When testing for differences between treatment means,a confidence interval is computed with ________.
A)the mean square error
B)the standard deviation
C)the sum of squared errors
D)the standard error of the mean
Q3) The alternative hypothesis used in ANOVA is H<sub>1</sub>: All population means are equal.
A)True
B)False
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14
Chapter 13: Correlation and Linear Regression
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Sample Questions
Q1) A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the independent variable?
A)Salesperson
B)Number of contacts
C)Amount of sales
D)Sales manager
Q2) The regression equation is = 29.29 0.96X,the sample size is 8,and the standard error of the slope is 0.22. What is the test statistic to test the significance of the slope?
A)z = 4.364
B)z = +4.364
C)t = 4.364
D)t = 0.960
Q3) The values of a and b in the regression equation are called the regression coefficients.
A)True
B)False
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15
Chapter 14: Multiple Regression Analysis
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Sample Questions
Q1) To evaluate the assumption of linearity,a multiple regression analysis should include
A)a calculation of variance inflation factors
B)hypothesis tests of individual regression coefficients
C)scatter diagrams of the dependent variable plotted as a function of each independent variable
D)an ANOVA table
Q2) In a regression analysis,three independent variables are used in the equation based on a sample of 40 observations. In the ANOVA table for a multiple regression analysis,what are the degrees of freedom associated with the F-statistic?
A)3 and 39
B)4 and 40
C)3 and 36
D)2 and 39
Q3) A correlation matrix shows individual correlation coefficients for all pairs of variables.
A)True
B)False
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16
Chapter 15: Nonparametric Methods: Nominal Level
Hypothesis Tests
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Sample Questions
Q1) The chi-square distribution is positively skewed.
A)True
B)False
Q2) To test if an observed frequency distribution with five classes is normally distributed,we need to ________.
A)compute an F-statistic
B)calculate a t-statistic
C)convert the class marks to standard normal z-statistics
D)convert the class limits to standard normal z-statistics
Q3) Suppose we test H<sub>0</sub>: <sub>1</sub> = <sub>2</sub> at the 0.05 level of significance. If the z-test statistic is 1.07,what is our decision?
A)Reject the null hypothesis.
B)Do not reject the null hypothesis.
C)Take a larger sample.
D)Reserve judgment.
Q4) For a contingency table,the expected frequency for a cell is found by dividing the row total by the grand total.
A)True
B)False
Page 17
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Chapter 16: Nonparametric Methods: Analysis of Ordinal
Data
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Sample Questions
Q1) A study was conducted on the percent of total advertising dollars spent by 10 local firms for advertising in the press and on cable television. Results were ranked with a resulting sum of squared differences equal to 128. What is the computed value of t?
A)0.719
B)0.804
C)1.339
D)0.650
Q2) Which of the following statements is true regarding the sign test?
A)It is based on the sign of the differences.
B)It is used with independent populations.
C)The chi-square is used as the test statistic.
D)The "T" statistic is the test statistic.
Q3) Which of the following values of Spearman's (rho)indicates the strongest relationship between two variables?
A)-0.91
B)-0.05
C)+0.64
D)+0.89
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Chapter 17: Index Numbers
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Sample Questions
Q1) The Bureau of the Census reported that the farm population dropped from 30.5 million in 1940 to 6.5 million in 1999. What is the index for 1999 based on 1940?
A)469.7
B)100.0
C)21.3
D)78.7
Q2) The CPI for "educational books and supplies" in June of 2006 was 386.7 (1982-1984 = 100). Interpret this index.
A)There was no significant increase in the price of "educational books and supplies."
B)The price of "educational books and supplies" increased 386.7 times.
C)If the average price of a textbook in 1982-1984 was $25.00,the CPI for "educational books and supplies" would predict that the price of the textbook in June 2006 would be $71.68.
D)If the average price of a textbook in 1982-1984 was $25.00,the CPI for "educational books and supplies" would predict that the price of the textbook in June 2006 would be $96.68.
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Chapter 18: Time Series and Forecasting
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Sample Questions
Q1) For the third quarter,the sales are 2,000 units; the seasonal index for the quarter is 1.15. What are the deseasonalized sales for the quarter?
A)1,739
B)2,015
C)2,115
D)115
Q2) If the exports (in million $)for the period 2006 through 2010 were $878,$892,$864,$870,and $912,respectively,what are these values called?
A)Moving average
B)Linear trend equation
C)Logarithmic trend equation
D)Time-series data
Q3) One component of a time series is cyclical variation. An example of cyclical variation is the business cycle that consists of periods of prosperity followed by periods of recession,depression,and recovery.
A)True
B)False
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Chapter 19: Statistical Process Control and Quality Management
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Sample Questions
Q1) A sampling plan states that if 20 incoming transistors are checked and 2 or less defects are found,the lot is accepted. If an incoming lot is 10 percent defective,what is the probability of accepting the lot of transistors?
A)0
B)1
C)0.677
D)0.333
Q2) What is usually developed to evaluate a sampling plan?
A)Frequency polygon
B)Scatter diagram
C)Operating characteristic curve
D)Simple bar chart
Q3) Random samples of four items are selected from a manufacturing process at regular intervals and a certain quality characteristic is measured. After 25 samples, X = 15,350 and R = 411.4. To construct a range chart,what is the LCL for the range?
A)602.004
B)411.400
C)625.666
D)0.000
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Chapter 20: An Introduction to Decision Theory
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Sample Questions
Q1) The manager of Paul's fruit and vegetable store is considering the purchase of a new seedless watermelon from a wholesale distributor. Because this seedless watermelon costs $4,will sell for $7,and is highly perishable,he expects only to sell between six and nine of them. What is the payoff value for the purchase of eight watermelons when the demand is for six watermelons?
A)17
B)21
C)24
D)10
Q2) The manager of Paul's fruit and vegetable store is considering the purchase of a new seedless watermelon from a wholesale distributor. Because this seedless watermelon costs $4,will sell for $7,and is highly perishable,he expects only to sell between six and nine of them. Based on a maximin decision strategy,what alternative is selected?
A)Order 6
B)Order 7
C)Order 8
D)Order 9
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