Statistics: Examination Scores, Sample Size, ANOVA, Regression Model

This article covers topics such as examination scores, sample size, ANOVA, and regression model in statistics. It includes relevant hypotheses, coefficient of determination, coefficient of correlation, and slope coefficient. It also discusses the significance of variables such as price and advertising in sales.

STATISTICS
STUDENT NAME/ID
[Pick the date]

Question 1
Examination scores
a. Frequency, cumulative frequency, relative frequency, cumulative frequency and percentage
frequency distribution with a class width of 10 for the examination scores is highlighted
below.
b. Histogram
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Skew is apparent as the left tail is shorter than the corresponding value of the right tail. The
skew presence represents that data is not normally distributed (Flick, 2015).
Question 2
a. Sample size (N) = Degree of freedom (dof) +1
Degree of freedom (dof) = 39+1 = 40
Hence,
Sample size (N) = 40 +1 = 41
Therefore, the sample size for the given scenario is 41.
b. Relevant hypotheses
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Unit price (slope coefficient) =0.029
Corresponding standard error = 0.021
Hence, t stat = (0.029/0.021) = 1.381
The hypothesis is two tailed. The p value = TDIST (1.38, 39, 2) = 0.175
Alpha (α) = 0.05
c. Coefficient of determination
4.8% changes in supply will be defined by changes in unit prices. The percentage is not
statistically significant and therefore, the regression model is not a good fit (Hair et. al., 2015).
d. Coefficient of correlation (R)
e. Supply for an unit price of X= $50,000
Question 3
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ANOVA
f. Relevant hypotheses
Test statistic =6.140,
Corresponding p value = 0.006
Alpha (α) = 0.05
Question 4
a. Regression model
Variables description
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Output
b. Relevant hypotheses
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Test statistic =6.7168
Corresponding p value (F significance) = 0.0526
Alpha (α) = 0.10
The p value is lesser than alpha which indicates that null hypothesis will be rejected. As a result,
alternative hypothesis will be accepted. Hence, the above shown regression model is significant
overall.
c. Hypothesis testing
Slope coefficient 1
Price (X1)
Slope coefficient 2
Advertising expenditure (X2)
Relevant hypotheses
Test statistic =3.098
Corresponding p value = 0.036
Alpha (α) = 0.10
The p value is lesser than alpha which indicates
that null hypothesis will be rejected. As a
result, alternative hypothesis will be accepted.
Hence, price is a significant variable for sales
(Hair et. al., 2015)..
Relevant hypotheses
Test statistic =0.040
Corresponding p value = 0.970
Alpha (α) = 0.10
The p value is more than alpha which indicates
that null hypothesis will not be rejected. As a
result, alternative hypothesis will not be
accepted. Hence, advertising is not a
significant for sale (Flick, 2015).
Significant Insignificant
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d. Regression model (rejecting the insignificant variable i.e. advertising from model)
e. The slope is indicative of the key factor that the sales will boost by 41.60 units only when
there is $1 increment in the price of the product (Flick, 2015).
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Reference
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. (2016) Essentials of
business research methods. 2nd ed. New York: Routledge.
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