Applying Statistical Tools for Business Decisions Analysis

This assignment demonstrates the application of statistical tools in business decision-making. It includes frequency distribution analysis of examination scores, ANOVA comparison of program effectiveness, and regression analysis to determine the relationship between sales, advertisement expenditure, and competitor pricing. The analysis uses MS Excel for calculations and graphical presentations, interpreting results to provide actionable recommendations, such as identifying the most effective program for employee enrollment and understanding the impact of competitor pricing on product sales. The assignment emphasizes statistical significance and uses p-values to validate conclusions, offering a comprehensive approach to data-driven business decisions.

Business Decisions by Statistical
Tools

Answer 1
a. The following Frequency distributions of examination scores were created using MS Excel.
Table 1: Frequency Distribution
Table 2: Cumulative Frequency Distribution
Table 3: Relative Frequency Distribution

Table 4: Cumulative Relative Frequency Distribution
Table 5: Percent Frequency Distribution
b. From percentage of students in view of their examination scores uncovered that the data in the
histogram was dispersed in the left tail but accumulated in the right tail. Collection of the
greater part of the understudies was seen above the class of examination score of 60 – 70
(Sullivan, 2015). Left skewness was apparent from the state of the histogram. It tends to be
deduced that understudies were getting great marks in examination.

Figure 1: Histogram of Percentage Distribution
Answer 3
a. Single factor ANOVA results were imported from Excel in Table 6.
Table 6: Comparison of Four Programs by ANOVA

b. From the single factor (program) ANOVA effectiveness of program C was apparent. The
descriptive value (M = 190 hours) of program C revealed that average output of day’s work
was for the C program was maximum among the four programs. The claim was established by
ANOVA where output from C program was significantly greater than that of from other three
programs (F = 6.14, p < 0.05) at 5% level of significance. The scholar suggested Allied
Corporation to enroll all of their employees in program C, where the decision was based on
the single factor ANOVA results (Brady et al., 2015).
Answer 4
a. Estimated regression equation at 10% level of significance was
Sales = 0 . 01∗Advertisement+ 41. 32 *Pr ice+3 .6
Table 7: Regression Model with Two Independent Variables at 10% Level of Significance

b. The regression model at 10% level of significance was significant overall (F = 6.72, p =
0.053). The p-value for the model was less than 0.1 (10% level of significance) suggesting the
significance of the model (Montgomery, Peck, and Vining, 2012).
c. The advertisement expenditure was not significantly related to sales of the product (t = 0.04, p
=0.97), and unit price of products of the competitors was significant (t = 3.1, p < 0.1) in
predicting sales of the product (Seber, and Lee, 2012).
d. From the previous model Advertisement cost was dropped and the new regression model was
constructed with competitors’ price as the single independent predictor of sales of the product
at 10% level of significance. The significant regression equation was evaluated as
Sales ( Y ) = 41 .60 *Pr ice ( X2 ) + 3 .58
Table 8: Regression Model with Price of Competitors as the Single Factor

e. Slope of unit price of competitors was 41.60 signifying that the angle of the slope was greater
than
π
4 . A highly positive correlation between competitors’ price and sales of product was the
implication of the range of the angle. Keeping other factors constant from regression equation
it was inferred that for one unit increase in competitors’ price would increase sales of
products by 41.60 units (George, and Mallery, 2016).
References
Brady, S.M., Burow, M., Busch, W., Carlborg, Ö., Denby, K.J., Glazebrook, J., Hamilton, E.S.,
Harmer, S.L., Haswell, E.S., Maloof, J.N. and Springer, N.M., 2015. Reassess the t test: interact
with all your data via ANOVA. The Plant Cell, pp.tpc-15.
George, D. and Mallery, P., 2016. Simple Linear Regression. In IBM SPSS Statistics 23 Step by
Step (pp. 205-217). Routledge.
Montgomery, D.C., Peck, E.A. and Vining, G.G., 2012. Introduction to linear regression
analysis (Vol. 821). John Wiley & Sons.
Seber, G.A. and Lee, A.J., 2012. Linear regression analysis (Vol. 329). John Wiley & Sons.
Sullivan III, M., 2015. Fundamentals of statistics. Pearson.