Business Research Module

This module covers statistical studies, t-test, ANOVA analysis, regression, correlation, experimental design, normal distribution, structural equation model and more.

Business Research Module
BUSINESS RESEARCH MODULE

Business Research Module
Question one
The diagram represents the process or stages of a statistical study. The first step involves
identification of the population from which to collect our data. Population refers to the total
count of objects or people that will be considered viable for our study.
The next step involves drawing a random sample from the population to be used for calculating
the parameters that are of interest. A sample refers to a smaller group of objects or people,
representing the large group, that will be admitted into the study.
The third stage of the process involves calculation of the statistic of interest basing on the data
that was collected from the population sample. Descriptive statistics, for example, mean, median
or proportions could be calculated at this stage.
The fourth and final stage involves interpretation and reporting the findings from the study. The
statistics calculated based on the sample responses could also be calculated by collecting data
from the whole population.
Question two
The table presents results of independent t test results for the variable RER. The independent-
samples t-test (or independent t-test, for short) compares the means between two independent
groups on the same continuous, dependent variable. The test to be performed is whether the
means are different or not. The null hypothesis for the independent t-test is that the population
means from the two independent groups are not different:
H0: u1 = u2
In most cases, it is being looked at to see if it can be shown that the null hypothesis is rejected
and the alternative hypothesis accepted, which is that the population means are not equal:
HA: u1 ≠ u2

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The Levene’s test for equality of variances presents a p-value greater than 0.05 implying that we
fail to reject the null hypothesis of equal variances. We therefore conclude that the variables
RER from the two groups under investigation are homoscedastic, that is they have equal
variances.
The independent t-test for equality of means has p-values greater than 0.05 when equal and
unequal variances are assumed. P-values greater than 0.05 imply that we fail to reject the
hypotheses of equal means when equal and unequal variances are assumed. We thereby conclude
that there is no difference in the means of the RER variable from the two population groups.
Question three
The table presents results of one-way ANOVA analysis. The one-way analysis of variance
(ANOVA) is used to determine whether there are any statistically significant differences between
the means of two or more independent (unrelated) groups. The null hypothesis for ANOVA is
that the mean (average value of the dependent variable) is the same for all groups. The
alternative or research hypothesis is that the mean is not the same for all groups.
The significant (p-value) is interpreted in order to either reject or fail to reject the null
hypothesis.
It can be seen that the significance (p-value) equals 0.022 which is less than 0.05, and therefore
at the 5% we reject the null hypothesis of no difference in the mean of the variable enjoyable in
the two groups. We therefore conclude that there is statistical difference in the enjoyable mean
for the two groups.

Business Research Module
Question four
The model summary table presents explanation on model variation;
On the off chance that the regression line isn't totally even, that is, in the event that the b
coefficient is not the same as 0, then some of the total variance is accounted for by the regression
line. This piece of the fluctuation is estimated as the aggregate of the squared differences
between the respondents’ predicted dependent variable values and the overall mean divided by
the number of respondents. By partitioning this clarified difference by the aggregate change of
dependent variable, we arrive at the proportion of the total variance that is accounted for by the
regression equation. This proportion varies between 0 and 1 and is symbolized by R2 (R Square).
R-square for our case is 0.762 implying that 76.2% of variance in the dependent variable is
explained by the independent variable. Adjusted R-square is 0.749 implying that when the model
is adjusted for extraneous predictors, 74.9% of variance in the dependent variable is explained by
the independent variable.
The second table is a regression ANOVA table;
The significance (p-value) is 0.000 implying that we reject the null hypothesis that there is no
difference in the means of the groups.
Question five

Business Research Module
The first model indicates that the constant has a p-value less than 0.05 implying that it is
significant to be included in the model. The variable X1 is 0.281 which is greater than 0.05
thereby it won’t be statistically significant to be include in the regression fit.
The second model shows that the constant and the variables X1 and X4 have p-values less than
0.05 implying that it would be statistically significant to include these variables in the model.
The fitted model shall therefore be given by;
Y 2=117.480+0.769 X 1−0.783 X 4
This implies that the independent variable x1 explains about 0.769 times of the dependent
variable, meaning that an increase in x1 by 1-unit results to an increase in Y2 by about 0.8 units.
The dependent variable is explained by -0.783 of x4, implying that an increase in x4 by 1-unit
results to a decrease in Y2 by about 0.783 units.
Question six
The table presents correlation coefficients between variables. Correlation measures association
between two or more variables. A positive value of correlation implies that variables are
positively correlated whereas a negative correlation value means that the variables are negatively
correlated.
The Pearson correlation p-values for association between job performance and IQ was found to
be less than 0.05 implying that the test of association is significant. The Pearson correlation
coefficient is 0.474 implying that IQ is positively correlated with job performance. The Pearson
correlation p-values for association between job performance and job motivation was found to be
less than 0.05 implying that the test of association is significant. The Pearson correlation

Business Research Module
coefficient is 0.635 implying that job motivation is positively correlated with job performance.
The Pearson correlation p-values for association between job performance and social support
was found to be less than 0.05 implying that the test of association is significant. The Pearson
correlation coefficient is 0.397 implying that social support is positively correlated with job
performance.
The Pearson correlation p-values for association between job motivation and IQ was found to be
greater than 0.05 implying that the there is no correlation between job motivation and IQ. The
Pearson correlation p-values for association between job performance and IQ was found to be
greater than 0.05 implying that there exists no association between the two variables.
The Pearson correlation p-values for association between motivation and social support was
found to be less than 0.05 implying that the test of association is significant. The Pearson
correlation coefficient is 0.363 implying that motivation is positively correlated with social
support.
Question seven
The table represents results of an experimental design showing main and interaction effects of
factors. The main effects are caused by each of the independent variables in the experiment
whereas the interaction effects are caused by interaction between the independent variables that
affect the dependent variable.
The p-value for the main effect due to the intercept is less than 0.05 implying that it is
statistically significant. The p-value for the main effect due to age is more than 0.05 implying
that age is statistically insignificant. The p-value for the main effect due to gender is less than
0.05 implying that it is statistically significant.

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The p-value for the interaction effect due to gender and age is greater than 0.05 implying that the
interaction between age and gender is statistically insignificant. Consequently. Age is not
dependent on gender and, gender is not dependent on age.
Question eight
The two curves represent one tailed tests of the normal distribution under the null hypothesis.
One-tailed tests are used for asymmetric distributions that have a single tail, such as the chi-
squared distribution. The null hypothesis H0 will be rejected when the p-value of the test statistic
is sufficiently extreme
Our test is not rejected if we find a test statistic is to the critical value. If the statistic is to the
right of the critical value, we reject the null hypothesis.
Our test statistic is found to be to the right of the critical value and the p-value is smaller than the
critical value, implying that we reject the null hypothesis conducted for our statistic.
Question nine
a) The variables of the first figure depict a direct linear positive relationship. The correlation can
be estimated to be 1, implying that an increase in the X variable by 1-unit results to a
corresponding increase in one unit of the Y variable.
The second figure shows that an increase in X variable does not result to an increase in the Y
variable. The correlation between the two values is therefore 0.
The third figure shows that an increase in the X variable by 1-unit results to a corresponding
decrease by 1 unit in the Y variable. The correlation can therefore be estimated to be -1.

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b) Beta values are estimated by estimating slope of the figures, that is change in Y divided by
change in X.
The beta value for the first slope can be estimated to be 1. The beta value of the second figure
can be estimated to be 0 and the beta value of the third figure can be estimated to be -1.
c) Equations of the lines of best fit
Figure 1: y=b 0+x+error
y=1+ x +error
Figure 2: y=b 0+0∗x+ error
y=3+ error
Figure 3: y=b 0±1∗x+ error
y=6−x +error
d) Relationship between correlation and regression
Correlation determines whether or not there exists an association between variables, and the
nature of such association if it exists, whether it is positive or negative.
On, the other hand regression predicts the value of the dependent variable given the value of the
independent variable, assuming that there exists a relationship between the variables.
If association exists, then the correlation value estimates the regression slope, when a line of best
fit is drawn on the data points.

Business Research Module
Question ten
The figure represents a structural equation model, which is a technique for modelling structural
relationships. It is a combination of factor analysis and multiple correlation analysis in a type of
causal modelling that incorporates various arrangement of numerical models, PC calculations,
and measurable strategies that fit systems of builds to information. When modelled with
conditions or speculation connections, you might demonstrate classes that speak to various
dimensions of significance or distinctive dimensions of deliberation. Given a reliance between
two classes, one class relies upon another however alternate class has no information of the one.
A change in one variable may affect other variables. kid acquires from its parent yet the parent
has no particular information of its youngsters. To put it plainly, reliance and speculation
connections are assymetric.
When you model with association relationships, you are demonstrating classes that are
companions of each other. Given a relationship between two classes, both depend on the other
here and there, and you can regularly explore in either heading. While reliance is an utilizing
relationship and speculation is an is-a-sort of relationship, an affiliation determines an auxiliary
way crosswise over which objects of the classes connect.
The figure depicts that achieve can be explained by the variables family and adjust or family and
cognitive. The dependent variable is therefore achieve and the independent variables are
cognitive, family and adjust. Cognitive and adjust have a direct effect on achieve whereas family
has an indirect effect on achieve.

Business Research Module