Holmes Institute HI6007 Statistics Group Assignment - Semester 2

This document presents a complete solution to a statistics assignment for the HI6007 course. The solution includes detailed calculations and explanations for each question. Question 1 covers the construction and interpretation of frequency distributions, cumulative frequency distributions, relative frequency distributions, and histograms to analyze examination scores. Question 2 delves into regression analysis, interpreting ANOVA output, hypothesis testing for the relationship between supply and unit price, calculating the coefficient of determination and correlation coefficient, and predicting supply based on unit price. Question 3 involves ANOVA table construction and hypothesis testing to compare group means. Finally, Question 4 focuses on regression modeling, hypothesis testing for the significance of model parameters (price and advertising), and interpreting the slope coefficient. The assignment utilizes MS Excel for calculations and graphical presentations, referencing relevant statistical concepts and methodologies.

STATISTICS
Student Name
[Pick the date]

Question 1
(a) Frequency distribution
(b) Histogram
Comment: It can be seen from the above histogram that examination score does not exhibit
normal distribution as it does not possess a bell curve. Further, a non-normal distribution is
confirmed from the presence of negative skew. It is also evident from the shape of histogram that
scores show significant deviations (Fehr and Grossman, 2013).
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Question 2
Variables
Supply (Y): Dependent variable
Unit price (X): Independent variable
ANOVA Output
(a) Sample size = Degree of freedom + 1 = (1+39) +1 = 41
(b) Null and alternative hypothesis
Slope coefficient (Unit price) = 0.029
Standard error (Unit price) = 0.021
The value of t stat =( 0.029
0.021 ) =1.381
Hypothesis test = Two tailed
The p value = ¿ TDIST (1.38 , 39 , 2)=0.175
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Given significance level = 5%
Fail to reject null hypothesis because p value is greater than significance level. Unit price and
supply is not associated (Harmon, 2016).
(c) Coefficient of determination
R2= SSR
SST = 354.68
(354.689)+(7035.262) = 354.68
7389.95 =0.048
Only 4.8% changes in supply would be offered explanation by change in unit prices. The
percentage is quite low and thus, the regression model would not be a good fit for analysis (Hair,
et.al., 2015).
(d) Correlation coefficient
R=¿
Only positive value of correlation coefficient would be taken as the sign of slope is positive.
Further, the strength of association between unit price and supply is weak only as the value is
lower than 0.5.
(e) Supply units for $50,000 unit prices.
Regression equation
Thus, supply will be 55526 units for $50,000 unit prices.
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Question 3
(a) ANOVA Table
(b) Hypothesis testing
Test statistic (F value) = 6.140
The p value = 0.006
Significance level = 5%
Reject the null hypothesis as p value is lower than significance level (0.006<0.05). Therefore,
sufficient witnesses are present to make the conclusion that at least one of the group mean would
be different (Harmon, 2016).
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Question 4
(a) Regression model by considering sales as dependent variable and product price and
advertising as independent variable.
(b) Hypothesis testing
Test statistic (F value) = 6.7168
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The significance F = 0.0526
Significance level = 0.10
Reject the null hypothesis as significance F is lower than significance level (0.0526<0.1).
Therefore, sufficient evidence is present to make the conclusion that the above model is
significant.
(c) Hypothesis testing
For Price
Null hypothesis H0: β price=0
Alternative hypothesis H1: β price ≠ 0
Test statistic (t value) = 3.098
The p value = 0.036
Significance level = 0.01
Reject the null hypothesis as p value is lower than significance level (0.036<0.1). Therefore,
sufficient evidence is present to make the conclusion that the slope coefficient (price) is
significant.
 For Advertising
Null hypothesis H0: β Advertising=0
Alternative hypothesis H1: β Advertising ≠ 0
Test statistic (t value) = 3.098
The p value = 0.970
Significance level = 0.1
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Fail to reject the null hypothesis as p value is greater than significance level (0.970>0.01).
Therefore, sufficient evidence is present to make the conclusion that the slope coefficient
(advertising) is not significant (Flick, 2015).
(d) Advertising: Insignificant variable and thus, can be taken away for the new model.
(e) Slope coefficient = 41.60
It implies that sales would be increased by 41.60 units when there is an increase in the price by 1
unit.
Reference
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Fehr, F. H. and Grossman, G. (2013) An introduction to sets, probability and hypothesis testing.
3rd ed. Ohio: Heath.
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.
Harmon, M. (2016) Hypothesis Testing in Excel - The Excel Statistical Master. 7th ed. Florida:
Mark Harmon.
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