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Statistics for Economists Reexamination deadline - ERASMUS Exercise 1

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Statistics for Economists

Reexamination deadline - ERASMUS

Exercise 1. Each student will solve 4 exercises from Beals — “Statistics for Economists” or from Newbold et al.- “Statistics for Business and Economics”, among those proposed to be solved at the end of the chapters, as follows:

e 1 exercise Newbold et al. chapter 6, pg. 277 - 279

*® 1 exercise from Beals, chapter 7, pg. 174 — 178

e 1 exercise from or Newbold et al., chapter 7 or chapter 8, pg. 324 — 326, pg. 343

— 344

e 1 exercise from Beals, chapter 8, pg. 206 — 210 or Newbold et al. chapter 9, 10,

 

pg. 378 — 382, pg. 49-412.

 

Remarks: the exercises must be different from those solved in class, and each student has to solve his/her own exercises. Furthermore, if an exercise contains numeric values you must replace the numerical values with your own values. Example: If you have an exercise that says “the mean price of an apartment is 65.....” you replace “65” with your own value.

 

Exercise 2. Each student will select her/his own sample, in SPSS, according to remark no. 3. You must have, in the database, at least two continuous variables, and at least two qualitative variables (these can be also obtained from continuous variables - use

Transform). Requirements:

 

a) Make a short research’s presentation: population under study, statistical unit,

the research’s objective, the sample size, describe a few (the most important) variables.

 

b) Univariate analysis: tables, graphs, descriptive statistics.

 

61) Analyze data for a qualitative variable: table of frequencies, bar chart, and mode.

 

62) Analyze data for a continuous quantitative variable (raw of data; scale): i) Graph:

Histogram; i) Central tendency: Mean, Median. Percentile: quartiles. Variation: standard deviation, variance, range. Shape of distribution: kurtosis and skewness.

 

SPSS. Analyze/Descriptive Statistics/Frequencies.

 

Specify, at each point (from b1, b2), what information bring the output statistics (i.e. interpret the results).

 

c) Choose a quantitative continuous variable X (related to the investigation’s objective):

c1) compute and interpret the confidence interval for mean of X, standard error SE, margin of error E. Analyze/Descriptive Statistics/Explore, c2) compute the sample size into be observed, if the accuracy is imposed to be as following: the probability P=0.95, the error E=5% from the mean of variable X (in the sample).

 

d) Consider a qualitative variable with two categories (0/1).

d7) Compute and interpret the confidence interval for the proportion; d2) compute the sample size nto be observed, for a probability P=0.99 and a margin of error E=3%.

 

e) Test a hypothesis concerning a mean. Analyze/ Compare means / One-

Sample T test

 

f) Test a hypothesis about a proportion. Analyze/ Nonparametric

Tests/Binomial

 

g) Test a hypothesis concerning the differences of two means. Analyze/

Compare means / independent-Samples T test.

 

For requirements e), f) and g) you have to explain how the results are obtained from

SPSS, and to interpret these results.

Exercise 3. For the sample selected in Exercise No.2:

 

a) Test a hypothesis using One Way Anova method: a1) choose the two variables properly, and indicate the null hypothesis #, ; a2) interpret the descriptive statistics and means plot, compute the test statistic F and explain shortly how are computed between

-groups sum of squares, within-groups and total sum of squares; a3) Use Levene’s test for homogeneity of variance, and concludes about adequate test, and about the null #, .

SPSS: Analyse/Compare Means/One-Way Anova. Options/Descriptive, Means plot,

Homogeneity of variance test, Bloown-Forsythe F test or the Welch's F test

 

b) Test a hypothesis using the Pearson chi-square test: a1) choose the two variables properly, and formulate the null hypothesis 4, ; a2) compute several expected frequencies; a3) measure the strength of the association, and conclude.

 

SPSS: Analyse/Descriptive Statistics/Crosstabs; Statistics: Chi-square, Contingency

coefficient, Cramers’V; Cells: Observed, Expected

 

c) Study the linear correlation between two variables: scatterplot, sign of correlation, test for non-significance. SPSS: Analysis/Correlate/Bivariate

 

d) Select a dependent variable Y and an independent (explanatory) variable X, suggested by economic theory: d1) estimate and interpret the coefficients of a linear regression model for Y; d2) compute predictions and residuals (errors) from the estimated model; compute and interpret the coefficient of determination. SPSS: Analyse/Regression/Linear.