Key Concept Exercise Research Methods Week 5: Inferential Statistical Analysis Question 1 The below table shows the results of an OLS regression of US real GDP growth rates (REALGDP) on changes of oil prices (OIL), interest rate (INTERESTRATE) and inflation rates (INFLATION) (monthly data from 1990 to 2013): REALGDP = CONSTANT + a OIL + b INTERESTRATE + c INFLATION CONSTANT OIL INTERSTRATE INFLATION Adj-R2 Coefficient 0.015 -0.037 -0.012 -0.004 58% T-stat 12.454 -4.565 -5.564 -1.56 p-value 0.000 0.003 0.032 0.145 (a) Discuss the statistical significance of the parameters, interpret the sign and magnitude of the estimates, and overall fit of the model. (b) Are the results in line with the predictions of the theory and why? Question 2 The below table shows the results of Mann-Whitney tests of comparing the distribution of productivity between male (1) and female (0), postgraduate (1) and undergraduate (0), and trained (1) and non-trained (0) employees, using independent samples from a company. Ranks SEX Productivity 2016 Laureate Education, Inc. N Mean Rank Sum of Ranks .00 28 25.48 713.50 1.00 25 28.70 717.50 Total 53 Page 1 of 4 Test Statisticsa Productivity Mann-Whitney U 307.500 Wilcoxon W 713.500 Z -.759 Asymp. Sig. (2-tailed) .448 Exact Sig. (2-tailed) .454 Exact Sig. (1-tailed) .227 Point Probability .003 a. Grouping Variable: SEX Ranks POSTGRAD Productivity N Mean Rank Sum of Ranks .00 25 20.72 518.00 1.00 28 32.61 913.00 Total 53 Test Statisticsa Productivity Mann-Whitney U 193.000 Wilcoxon W 518.000 Z -2.804 Asymp. Sig. (2-tailed) .005 Exact Sig. (2-tailed) .004 Exact Sig. (1-tailed) .002 Point Probability .000 a. Grouping Variable: POSTGRAD Ranks TRAINING Productivity 2016 Laureate Education, Inc. N Mean Rank Sum of Ranks .00 25 24.24 606.00 1.00 28 29.46 825.00 Total 53 Page 2 of 4 Test Statisticsa Productivity Mann-Whitney U 281.000 Wilcoxon W 606.000 Z -1.233 Asymp. Sig. (2-tailed) .218 Exact Sig. (2-tailed) .221 Exact Sig. (1-tailed) .111 Point Probability .002 a. Grouping Variable: TRAINING (a) Discuss critically the results of the hypothesis that the distribution of productivity of male employees is equal to the distribution of productivity of female employees, the distribution of productivity of graduate employees is equal to the distribution of productivity of undergraduate employees, and the distribution of productivity of trained employees is equal to the distribution of untrained employees. (b) What are the underlying assumptions of the Mann-Whitney test? Explain if, in your opinion, those are met in the above examples. Question 3 A company wants to produce three different mobile phones, with low-range, mid-range and high-range specifications, respectively. A survey with 100 respondents has been used to reveal the choices of potential customers. The company wants to review the figures to see if the three mobile phones would be equally popular. The results of the Chi-Square test are given in the following tables: MOBILE Observed N Expected N Residual 1.00 31 33.3 -2.3 2.00 45 33.3 11.7 3.00 24 33.3 -9.3 Total 100 2016 Laureate Education, Inc. Page 3 of 4 Test Statistics MOBILE 6.860a Chi-Square df 2 Asymp. Sig. .032 a. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 33.3. Use the information provided in the tables to: (a) Describe the null hypothesis for the Chi-Square test. (b) Discuss the results and explain whether there are statistically significant differences in the preference for the three devices. (c) What are the underlying assumptions of the Chi-Square test? Explain if, in your opinion, those are met in the above examples. Question 4 An institute conducted a survey where a sample of 50 people were asked whether or not have been promoted to a better job in their industry during the last 24 months. For each respondent, the variables AGE, EXPERIENCE (years of employment in the industry) and SEX (i.e. male (1) or female (0)) are recorded. A logistic regression was then used to estimate the probability of a promotion within 24 months as a function of the variables. The estimation results are shown below: Variables in the Equation B a Step 1 S.E. Wald df Sig. Exp(B) AGE .035 .036 .940 1 .332 1.035 EXPERIENCE .148 .107 1.908 1 .167 1.159 -.986 .672 2.154 1 .142 .373 -1.866 1.196 2.436 1 .119 .155 SEX Constant a. Variable(s) entered on step 1: AGE, EXPERIENCE, SEX. (a) Use the information in the table to discuss the sign, magnitude and statistical significance of the coefficients. (b) Would you consider the model as a good tool for predicting promotions? Why? 2016 Laureate Education, Inc. Page 4 of 4