Statistical Methods for Economics
Pre-Test Questions
Course Introduction
Statistical Methods for Economics introduces students to the fundamental concepts and techniques of statistics as applied to economics. The course covers topics such as descriptive statistics, probability theory, sampling distributions, estimation and hypothesis testing, regression analysis, and the interpretation of economic data. Emphasis is placed on using statistical methods to analyze real-world economic issues, making data-driven decisions, and critically evaluating empirical research. Students will gain practical experience through problem-solving and the use of statistical software, equipping them with essential analytical tools for careers in economics and related fields.
Recommended Textbook
Statistics for Business and Economics 8th Edition by Betty Newbold
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Chapter 1: Describing Data: Graphical
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Sample Questions
Q1) What statistical term describes the 30 plots?
Answer: Sample
Q2) Construct a frequency histogram of the data.
Answer: 11ea5b8a_b6af_55e4_b1f3_3be6330b0335_TB2968_00
Q3) A student's IQ is an example of the ratio scale of measurement.
A)True
B)False
Answer: False
Q4) If the sample is a good representation of the population,what percentage of those who did poorly on the final exam should we expect to have spent the weekend studying?
Answer: 15 out of 68,or 22.06%
Q5) The statement "The price of a Canon digital camera is likely to be lower in three months than it is now" is arrived at by the use of descriptive statistics.
A)True
B)False
Answer: False
Q6) Construct a pie chart to show this information.
Answer: 11ea5b8a_b6b1_ee00_b1f3_d36506513008_TB2968_00
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Chapter 2: Describing Data: Numerical
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Sample Questions
Q1) The median can be determined for any set of ordinal,interval or ratio-level data.
A)True
B)False
Answer: True
Q2) Which measures of central tendency are not affected by extremely small or extremely large values?
A)arithmetic mean and median
B)arithmetic mean and mode
C)arithmetic mean and geometric mean
D)median and mode
Answer: D
Q3) What conclusions can you draw about the relationship between weight and fuel efficiency?
Answer: In general,there is a negative relationship between the two variables;that is,as the weight of the SUV increases,the gas mileage per gallon (SUV efficiency)decreases.
Q4) Calculate the mean score in sample 2.
Answer: 11ea5b8a_b6dd_9297_b1f3_c147cb42eb62_TB2968_11 <sub>2</sub> =12.625
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Chapter 3: Probability
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Sample Questions
Q1) Calculate P(A<sub>1</sub> B<sub>2</sub>).
Answer: P(A<sub>1</sub> B<sub>2</sub>)= P(A<sub>1</sub> B<sub>2</sub>)/ P(B<sub>2</sub>)= 0.10 / 0.40 = 0.25
Q2) What is the probability that a consumer who had high awareness of the ad campaign ranked the product as good?
A)0.675
B)0.385
C)0.775
D)0.325
Answer: A
Q3) If the union of several events covers the entire sample space,it is said these events are:
A)mutually exclusive.
B)mutually related.
C)mutually apart.
D)collectively exhaustive.
Answer: D
Q4) Calculate P(B D).
Answer: P(B D)= P(D|B)P(B)= (0.60)(0.30)= 0.18
Page 5
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Chapter 4: Discrete Random Variables and Probability
Distributions
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Sample Questions
Q1) The variance of the sum of two random variables is the sum of their variances plus two times the covariance.
A)True B)False
Q2) Calculate E(X + Y)and Var(X + Y)directly by using the probability distribution of X + Y.
Q3) What is the probability that more than three of them will retire this year? Use the Poisson approximation to the binomial.
Q4) A discrete random variable is a random variable if it can take on an infinite number of values.
A)True B)False
Q5) Compute the mean for the linear function W = 2X + Y.
Q6) Computation of marginal probabilities,means,and variances for jointly distributed random variables cannot be developed using a computer package.
A)True B)False
Q7) Compute the expected value for X.
Q8) Are X and Y independent? Explain.
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Chapter 5: Continuous Random Variables and Probability
Distributions
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Sample Questions
Q1) Suppose that 19% of all sales are for amounts greater than $1,000.In a random sample of 30 invoices,what is the probability that more than six of the invoices are for over $1,000? Use the binomial approximation for the normal distribution.
A)0.4443
B)0.9440
C)0.5557
D)0.0560
Q2) Find the probability that the percentage of successes is greater than 0.42
Q3) What is the probability that you have to wait between 10 and 15 minutes?
Q4) What is the probability that a soccer game goes for 45 minutes without either team scoring?
Q5) Find the probability that the percentage of successes is between 0.38 and 0.43
Q6) Find the probability that the percentage of successes is less than 0.37
Q7) If the covariance of two random variables X and Y is positive,then Var(X - Y)will be larger than Var(X + Y).
A)True
B)False
Q9) What is the 95<sup>th</sup> percentile of this normal distribution? Page 7
Q8) Find the probability that the number of successes is greater than 775.
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Page 8
Chapter 6: Sampling and Sampling Distributions
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Sample Questions
Q1) What is the standard error of the sample proportion?
Q2) If a sample of size 100 is taken from a population whose standard deviation is equal to 100,then the standard error of the mean is equal to:
A)10
B)100
C)1,000
D)10,000
Q3) What is the probability that the mean number of points you receive on four flips is 0?
Q4) Without doing the calculations,state whether a larger or smaller sample would be required to guarantee that the probability that the sample mean differs from the population mean by more than 2.1 hours is less than 0.10,when compared to the sample needed to ensure that the probability that the sample mean differs from the population mean by more thatn 2.1 hours is less than 0.05.
Q5) What is the probability that for a sample of 25,the average amount spent exceeds $60?
Q6) What is the probability that the sample mean exceeds the population mean by more than 2.1 hours?
Q7) Find the probability that the sample standard deviation is less than 2.6.
Page 9
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Chapter 7: Estimation: Single Population
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Sample Questions
Q1) Calculate the width of the 95% confidence interval estimate.
A)16.12
B)11.38
C)17.86
D)13.58
Q2) In a survey of 472 personnel directors,63% thought that they would be hiring new personnel over the next three months.Which of the following represents a 98% confidence interval for the proportion of all personnel directors planning to hire personnel over the next three months?
A)0.63 ± 0.057
B)0.63 ± 0.047
C)0.63 ± 0.042
D)0.63 ± 0.052
Q3) Find the lower confidence limit of the 99% confidence interval.
A)340.25
B)325.98
C)319.59
D)332.41
Q4) Calculate the width of the 90% confidence interval estimate for the population proportion in favor of this policy.
10
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Chapter 8: Estimation: Additional Topics
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Sample Questions
Q1) What is the sample variance of the Group 2?
A)468.70
B)366.01
C)456.19
D)490.67
Q2) Based on the 95% confidence interval for the difference between the two population proportions,is there evidence that the population proportions are different?
Q3) Find the width of the 98% confidence interval.
A)5.46
B)3.64
C)0.91
D)0.60
Q4) Find the margin of error for a 95% confidence interval for the difference in the means of the two populations.
Q5) Find a 95% confidence interval for the difference in average functioning time before recharging the two models.
Q6) Find a 95% confidence interval for the difference between the two population proportions.
Q7) Find the width of the 99% confidence interval.
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Chapter 9: Hypothesis Testing: Single Population
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Sample Questions
Q1) A fitness club claims that the average age of its members is 42.Assume that the ages are normally distributed.You believe that the average age is less than 42,therefore,you ask the ages of a few of the fitness club's members and get the following values: 40,55,50,33,38,35,30,and 45.Do you have any reason at the 10 per cent level of significance to think the fitness club's claim is incorrect?
Q2) Test at the 5% level the null hypothesis H<sub>0</sub> : 42,000 against the alternative hypothesis
H<sub>1</sub> : < 42,000
Q3) Which distribution is most appropriate to perform this hypothesis test?
A)Student's t distribution
B)Normal distribution
C)F distribution
D)Chi-square distribution
Q4) When testing H<sub>0</sub> : = 50 against H<sub>1</sub> : 50,where would the rejection region fall for this hypothesis test?
A)in the left tail
B)in the right tail
C)in both the left and right tails
D)at point zero
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Chapter 10: Hypothesis Testing: Additional Topics
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Sample Questions
Q1) Suppose that a t test of H<sub>0</sub> : <sub>1</sub> - <sub>2</sub> = 0 against H<sub>1</sub> : <sub>1</sub> - <sub>2</sub> 0 is based on 15 degrees of freedom.If the calculated value of the test statistic is t = -1.75,then the p-value for this test is approximately 0.10.
A)True
B)False
Q2) In order to test if the diet is effective,what is the appropriate critical value(s)at the 0.05 level of significance?
A)2.131
B)2.120
C)1.753
D)1.746
Q3) Use statistical software to determine whether these data are sufficient to infer at the 10% significance level that the two population means differ.
Q4) Using results of Excel or Minitab to conduct a two-sample t-test,test H<sub>0</sub> : <sub>1</sub> - <sub>2</sub> 0 vs.H<sub>1</sub> : <sub>1</sub><sub>2</sub> > 0 at the 5% significance level.
Q5) What is the test statistic?
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Chapter 11: Simple Regression
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Sample Questions
Q1) In a regression problem the following pairs of (x,y)are given: (2,1),(2,-1),(2,0),(2,-2)and (2,2).Which of the following is true of the given data?
A)For the given data,the coefficient of correlation is -1.
B)For the given data,the coefficient of correlation is 0.
C)For the given data,the coefficient of correlation is 1.
D)For the given data,the coefficient of correlation is 2.
Q2) When we compute the sample correlation r from data,the result will be definitely zero when the population correlation is zero.
A)True
B)False
Q3) Develop a 90% confidence interval for the population slope if the following regression information are given: b<sub>1</sub>= 23.5,p-value = 0.01,and n = 25.
A)23.5 ± 17.35
B)23.5 ± 15.35
C)23.5 ± 16.35
D)23.5 ± 14.35
Q4) Explain the difference between the residual e<sub>i</sub> and the model error <sub>i</sub>.
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Chapter 12: Multiple Regression
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Sample Questions
Q1) What is the 95% confidence interval for <sub>1</sub>?
A)2)13 ± 4.17
B)4)59 ± 4.38
C)2)13 ± 4.38
D)4)59 ± 4.17
Q2) In a multiple regression model,the mean of the probability distribution of the error variable, <sub>i</sub>,is assumed to be:
A)1.0
B)0.0
C)any value greater than 1.
D)K,where K is the number of independent variables included in the model.
Q3) What would you forecast the occupancy rate to be this July when we expect 525,000 visitors? We would anticipate the room rate to average $130 and consumer confidence to be 110.
Q4) Interpret the coefficient b<sub>1</sub>.
Q5) For a fixed weekly income,test the null hypothesis that milk consumption does not depend linearly on the size of the family against an appropriate one-sided alternative.Use = 0.025.
Q6) Compute the mean squares for regression.
Page 15
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Chapter 13: Additional Topics in Regression Analysis
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Sample Questions
Q1) Suppose you want to estimate the model Y = <sub>0</sub> + <sub>1</sub>X<sub>1</sub> + <sub>2</sub>X<sub>2</sub> + <sub>3</sub>X<sub>3</sub> + <sub>4</sub>X<sub>4</sub>.However,you cannot measure X<sub>4</sub>,so you estimate Y = <sub>0</sub> + <sub>1</sub>X<sub>1</sub> + <sub>2</sub>X<sub>2</sub> + <sub>3</sub>X<sub>3</sub> instead.This is an example of regression result that will be subject to:
A)autocorrelation.
B)heteroscedasticity.
C)multicollinearity.
D)specification bias.
Q2) Is there sufficient evidence at the 1% significance level to conclude that the interaction term should be retained?
Q3) Model specification includes selection of the dependent and independent variables and the algebraic form of the model.
A)True
B)False
Q4) What problems can occur when the independent variables are correlated with each other?
Q5) Test the model for autocorrelated errors.
Page 16
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Chapter 14: Analysis of Categorical Data
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Sample Questions
Q1) A chi-square test of association in a contingency table with r rows and c columns has a chi-square distribution with rc-1 degrees of freedom.
A)True
B)False
Q2) Consider a chi-square distributed random variable with 12 degrees of freedom and a significance level of 0.025.The chi-square value from the table is 23.337.Which of the following computed values of the chi-square test statistic would lead us to a decision "fail to reject" the null hypothesis?
A)41.47
B)17.12
C)32.59
D)26.43
Q3) The Wilcoxon rank sum test statistic "T" is approximately normally distributed whenever the sample sizes are larger than:
A)10
B)5
C)9
D)8
Q4) What is the Spearman's rank correlation for this data?
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Chapter 15: Analysis of Variance
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Sample Questions
Q1) If a level of significance of 0.05 is chosen,what is your conclusion?
Q2) In a one-way ANOVA,all the populations may or may not be normally distributed.
A)True
B)False
Q3) How many experimental units were in this study?
Q4) Complete the ANOVA table.
Q5) Compute mean squares for within groups.
Q6) The value of the test statistic F is equal to:
A)1.95
B)1.89
C)2.09
D)2.04
Q7) The F distribution cannot be used with a two-way ANOVA.
A)True
B)False
Q8) The Mann-Whitney test is a nonparametric alternative to the one-way analysis of variance.
A)True B)False
Q9) Calculate the Kruskal-Wallis test statistic. Page 18
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Chapter 16: Time-Series Analysis and Forecasting
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Sample Questions
Q1) Determine the forecast for the year 1901.
A)104.95
B)98.50
C)102.25
D)90.31
Q2) The Holt-Winters Exponential Smoothing procedure allows only the trend component in a time series.
A)True
B)False
Q3) What is the value of mean absolute deviation?
A)17.28
B)30.55
C)1534.28
D)3451.28
Q4) Calculate the seasonally adjusted value for x<sub>18</sub>.
A)91.52
B)0.9464
C)84.53
D)0.6967
Q5) Use the seasonal index method to seasonally adjust this series.
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Chapter 17: Additional Topics in Sampling
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Sample Questions
Q1) Estimate the mean monthly expenditures.
A)78.26
B)73.74
C)59.82
D)64.67
Q2) Find a 90% confidence interval for the total expenditures.
Q3) Estimate the total expenditures for the population.
Q4) Find a 90% confidence interval for the mean rating given by all freshmen and sophomores on the campus.
A)3.98 ± 0.592
B)3.98 ± 0.229
C)3.98 ± 0.712
D)3.98 ± 0.456
Q5) The drawback of quota sampling is that,since the sample is not chosen using probabilistic methods,there is no valid way of determining the reliability of the resulting estimates.
A)True
B)False
Q6) Estimate the total sales for the corporation based on these estimates.
Q7) Find a 90% confidence interval for the population.
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