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
Coefficient T-stat p-value
CONSTANT 0.015 12.454 0.000
OIL -0.037 -4.565 0.003
INTERSTRATE -0.012 -5.564 0.032
INFLATION -0.004 -1.56 0.145
Adj-R2 58%
(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 N Mean Rank Sum of Ranks
Productivity .00 28 25.48 713.50
1.00 25 28.70 717.50
Total 53
© 2016 Laureate Education, Inc. Page 2 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 N Mean Rank Sum of Ranks
Productivity .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 N Mean Rank Sum of Ranks
Productivity .00 25 24.24 606.00
1.00 28 29.46 825.00
Total 53
© 2016 Laureate Education, Inc. Page 3 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 4 of 4
Test Statistics
MOBILE
Chi-Square 6.860a
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 S.E. Wald df Sig. Exp(B)
Step 1a AGE .035 .036 .940 1 .332 1.035
EXPERIENCE .148 .107 1.908 1 .167 1.159
SEX -.986 .672 2.154 1 .142 .373
Constant -1.866 1.196 2.436 1 .119 .155
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?
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