Part 1:
Conduct a T-test:
a. What is the question you are asking?
The question being asked is there is a relationship between the absorbance readings from North Branch Chicago River Site and absorbance readings from North Shore Channel Site.
b. What is your null hypothesis?
The null hypothesis is that there are no relationship between the absorbance readings from North Branch Chicago River Site and absorbance readings from North Shore Channel Site.
c. What is the alternative hypothesis?
The alternative hypothesis is that there is a relationship between the absorbance readings from North Branch Chicago River Site and absorbance readings from North Shore Channel Site.
B. Calculate the test statistic (t-stat):
The formula below was used to calculate the t-stat of the data collected for this exercise.
Where:
The tables below show a summary of the analysis carried out for each data values.
Table 1: Average and variance for absorbance readings from North Branch Chicago River Site
Table 2: Average and variance for absorbance readings from North Shore Channel Site
Applying the formula:
t = 0.67225/ 0.06462
=10.4
C. Degrees of freedom:
Degrees of freedom for each group is n-1
4 - 1 = 3 for absorbance readings from North Branch Chicago River Site.
4 – 1 = 3 for absorbance readings from North Shore Channel Site.
Degrees of freedom = 3 + 3 = 6.
D. Using the t-stat and degrees of freedom, estimate the p-value:
Significance level = 0.05.
Probability (one-tailed) = 0.02315.
E. Based on the p-value:
Based on the p-value which has been estimated we cannot reject the null hypothesis. This is mainly because when the p-value is less than the significance level it means that there is a relationship between the absorbance readings from North Branch Chicago River Site and absorbance readings from North Shore Channel Site.
Part 2: Results
The tables below shows the data collected:
Range finding
The chart shows the relationship between absorbance and dilution levels.
Below is the line and equation of best fit for the data collected. It also shows the correlation value for the data.
y = 2.133x - 0.052.
R² = 0.855.
Below are the results that were used for the t-test analysis in part 1.
Table 1: Absorbance readings from North Branch Chicago River Site Absorbance
Table 2: Absorbance readings from North Shore Channel Site Absorbance
Table 3: Absorbance readings for Standard Curve Concentration (mg/l) Absorbance
Works Cited:
Ott, Lyman, and Michael Longnecker. An Introduction to Statistical Methods and Data Analysis. Belmont, CA: Brooks/Cole Cengage Learning, 2010. Print.
Ryan, Thomas P. Statistical Methods for Quality Improvement. Hoboken, N.J: Wiley, 2011. Print.
