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# Probability & Statistic Problems - ANOVA, Correlation Coefficient, and Linear Equation

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Probability & Statistics:

Problem 1:
Six samples of four types of milk were analyzed to determine protein content. The results where the following (ug/mL):
Tres Monjitas® 5.2 4.5 6.0 6.1 6.7 5.8
Suiza Dairy® 6.5 8.0 6.1 7.5 5.9 5.6
Mayagüez Dairy® 5.8 4.7 6.4 4.9 6.0 5.2
Indulac® 8.3 6.1 7.8 7.0 5.5 7.2

Using the ANOVA method at a significance level of 0.05, test if there exist a difference between the content percent of protein of the different labels of milk above.

Problem 2:
In water treatment plants the level of turbidity (y), is suspected that is linear to the relation of inches of rain water accumulated through the month, (x). The following information of the water treatment plant is available as follows:

Level of Turbidity (y) 1 2 3 4 5 6
Inches of rain water (x) 5.6 4.6 4.5 3.7 3.2 2.7

a. Find the linear equation using the square method minimum which best describes the data above.
b. Calculate the correlation coefficient.

##### Solution Summary

The solution determines the ANOVA, correlation coefficient, and linear equation.

##### Solution Preview

Please see the attached files. The word document contains the solutions, while the Excel spreadsheet are attached as well.

Probability & Statistics:
Problem 1:
Six samples of four types of milk were analyzed to determine protein content. The results where the following (ug/mL):
Tres Monjitas® 5.2 4.5 6.0 6.1 6.7 5.8
Suiza Dairy® 6.5 8.0 6.1 7.5 5.9 5.6
Mayagüez Dairy® 5.8 4.7 6.4 4.9 6.0 5.2
Indulac® 8.3 6.1 7.8 7.0 5.5 7.2
Using the ANOVA method at a significance level of 0.05, test if there exist a difference between ...

Solution provided by:
###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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