Group Assignment: Statistical Analysis and Interpretation

This statistics assignment provides solutions to problems involving frequency distribution, histograms, and identifying outliers. It addresses hypothesis testing related to correlation between demand and unit price using ANOVA, calculating R-squared and correlation coefficients. The assignment also explores hypothesis testing for the equality of population means using ANOVA. Furthermore, it delves into multiple regression analysis, including calculating degrees of freedom, testing the significance of slope coefficients for phone prices and advertising spots, and interpreting the results. The solutions include detailed calculations, interpretations, and references to relevant statistical concepts and methods.

STATISTICS
GROUP ASSIGNMENT
Student Name
[Pick the date]

Question 1
(a)
 Frequency distribution table
(Relative frequency, percentage relative frequency with class width of $50)
(b)
 Histogram
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It is apparent that right tail length is significantly greater than left tail length which is indicative
of the graph being asymmetric. Also, it is possible that some values on the high side may be
unusually high and hence termed as outliers (Hair et. al., 2015)
(c) The possibility of presence of outliers is confirmed from the above discussion. In such a
scenario, deploying mean as the appropriate central tendency measure would not be advisable.
This is because the mean has the tendency to get skewed owing to outliers on either side. Hence,
more appropriate measure of central tendency would be provided by median whose computation
is independent of the values of the extreme data (Eriksson and Kovalainen, 2015).
Question 2
(a)
Hypotheses
Demand and unit price are correlated or not.
ANOVA
Key aspects
The test stat (t value) for x (slope coefficient: Unit price) = -8.617
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P value for x (slope coefficient: Unit price) = 0.00
Alpha (level of significance) = 5% or 0.05
Conclusion
The p value << alpha and thus, reject H0 and accept H.
This provides clear indication that there is a statistically significant relationship between the
selected variable i.e. demand and unit price.
(b)
Calculation for R square (Coefficient of determination)
SST
Thus, 9
The above value highlights the fact that the given regression model is capable to account for
61.7% of the variation witnessed in the dependent variables i.e. demand. Hence, unit price
cannot offer explanation for about 38.3% of variation observed in demand (Flick, 2015).
(c)
Calculation for R (Coefficient of correlation)
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The correlation coefficient may assume any of the value depending on the nature of the
relationship. There is an inverse relationship that exists in this case which is apparent from the
negative sign attached to the regression slope coefficient. Therefore, correlation coefficient
would assume a value of -0.786 (Hillier, 2016).
Question 3
Hypotheses
The mean of all the three population are same or not.
Key aspects
The test stat (F value) = 25.89
P value (significance F) = 0.00
Alpha (level of significance) = 5% or 0.05
Conclusion
The p value << alpha and thus, reject H0 and accept H. Therefore, the appropriate inference that
can be drawn is that atleast one population average would be different in a statistically
significant way from the other two (Eriksson and Kovalainen, 2015).
Question 4
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(a)
Regression equation
(b)
Calculation for degree of freedom
Data collected = 7 days
Dof for regression = 2
Dof for residual = 4
Hypotheses
Slope coefficients are statistically significant or not.
Key aspects
The test stat (F value) = 80.1181
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P value (significance F) = 0.00
Alpha (level of significance) = 5% or 0.05
Conclusion
The p value << alpha and thus, reject H0 and accept H. The given regression model would be
considered statistically significant considering that all the slope coefficients cannot be assumed
to be zero or insignificant (Flick, 2015).
(c)
Hypothesis
Phone prices are statistically significant or not.
Key aspects
The test stat (t value) = 1.0780
P value = 0.2060
Alpha (level of significance) = 5% or 0.05
Conclusion
The p value >> alpha and thus, there is failure to reject H0. The slope coefficient for the price
independent variable can be assumed to be zero and thereby lacks any statistical significance
(Hillier, 2016).
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 Hypothesis
Advertising spots are statistically significant or not.
Key aspects
The test stat (t value) = 12.23
P value = 0.00
Alpha (level of significance) = 5% or 0.05
Conclusion
The p value << alpha and thus, reject H0 and accept H1. The slope coefficient associated with
advertising spots cannot be taken as zero and hence has a statistically significant impact on daily
mobile sales (Eriksson and Kovalainen, 2015).
(d)
The above slope coefficient hints at increase in daily mobile sales by 0.4733 units when there is
an advertisement spot increase by 1 unit (Hair et. al., 2015).
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(e)
=?
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References
Eriksson, P. and Kovalainen, A. (2015) Quantitative methods in business research 3rd ed.
London: Sage Publications
Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research
project. 4th ed. New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015) Essentials of
business research methods. 2nd ed. New York: Routledge.
Hillier, F. (2016) Introduction to Operations Research. 6th ed. New York: McGraw Hill
Publications.
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