Quantitative Methods Assignment: Winery Alcohol Content Analysis

This assignment focuses on analyzing winery data using quantitative methods. Question 1 examines the variation in alcohol content of Pinot Noir wines based on the origin of the grapes, employing ANOVA to determine if there is a statistically significant difference in alcohol levels across different wineries. Question 2 investigates the association between the closing prices of Apple and Microsoft common stocks using Spearman rank correlation coefficient, exploring the strength and direction of the relationship. The assignment includes hypothesis testing, calculation of statistical values, and interpretation of results, including the identification of Type 1 and Type 2 errors. The student provides detailed answers, tables, and interpretations of the statistical analyses.

Running head: QUANTATIVE METHODS
Quantative Methods
Name of the Student
Name of the University
Author Note:

1QUANTATIVE METHODS
Table of Contents
Answer to the q. no. 1(a)............................................................................................................2
Answer to the q. no. 1(b)............................................................................................................2
Answer to the q. no. 1(c)............................................................................................................3
Answer to the q. no. 2(a)............................................................................................................3
Answer to the q. no. 2(b)............................................................................................................4
Answer to the q. no. 2(c)............................................................................................................4
Answer to the q. no. 2(d)............................................................................................................4
References..................................................................................................................................5

2QUANTATIVE METHODS
Answer to the q. no. 1(a)
Figure 1 Column Scatterplot
Table 1 Mean and Variation table
Table 2 ANOVA table
Answer to the q. no. 1(b)
H0: Alcohol content does not varies by grape origin.

3QUANTATIVE METHODS
i.e. μ1=μ2=μ3=μ4 =μ5
H1: Alcohol content varies by grape origin.
i.e. μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5
Alpha Value = 0.05
P- Value = 0.06
It has been seen that the P- Value is larger than the alpha value. Hence the testing hypothesis
is not significant. Therefore there is a sufficient evidence at 5% level of significance to
conclude that Alcohol content does not varies by grape origin.
Answer to the q. no. 1(c)
Table 3 ANOVA table
F = MS between groups
MS within groups
MS= SS
df
Answer to the q. no. 2(a)
Table 4 Spearman rank correlation coefficient
Degrees of freedom = 11-2
= 9

4QUANTATIVE METHODS
Spearman rank correlation coefficient ( ρs) = 1- 6 ∑ d2
n(n2 −1)
= 1- 6∗107
11(121−1)
ρs = 0.5
There is a positive association between Apple and Microsoft common stock closing
prices.
Answer to the q. no. 2(b)
It has been seen that ρs = 0.5. That means spearman rank correlation coefficient is
positive. Hence it can be conclude that there is a positive association between Apple and
Microsoft common stock closing prices.
Answer to the q. no. 2(c)
H0: Spearman rank correlation coefficient is greater than and equal to 0.6
i.e. ρs ≥ 0.6
H0: Spearman rank correlation coefficient is less than 0.6
i.e. ρs ¿ 0.6
Alpha Value = 0.05
P- Value = 0.12
It has been seen that P- Value = 0.12. Hence the test hypothesis is significant.
Therefore there is a sufficient evidence at 5% level of significance to conclude that Spearman
rank correlation coefficient is less than 0.6.
Answer to the q. no. 2(d)
Type 1 error means if the hypothesis or statement is true but it is rejected.
Type 2 error means if the hypothesis or statement is false but it is accepted.
According to this example of association between Apple and Microsoft common
stock closing prices the type 1 and type 2 error statement as stated as bellow
It has been illustrated that
ρs = 0.5
The Spearman rank correlation coefficient is greater than and equal to 0.6. It is false.
That means if this statement has been accepted then it is called type 2 error.
Again Spearman rank correlation coefficient is less than 0.6. The statement is true.
Now if the hypothesis or statement has been rejected then it is called type 1 error.

5QUANTATIVE METHODS
References
Okada, K., 2013. Is omega squared less biased? A comparison of three major effect size
indices in one-way ANOVA. Behaviormetrika, 40(2), pp.129-147.
Sedgwick, P., 2014. Spearman’s rank correlation coefficient. Bmj, 349, p.g7327.