Problem 1 Cold Storage started its operations in Jan 2016. They are in the business of storing Pasteurized Fresh Whole or Skimmed Milk, Sweet Cream, Flavored Milk Drinks. To ensure that there is no change of texture, body appearance, separation of fats the optimal temperature to be maintained is between 2 deg - 4 deg C. In the first year of business they outsourced the plant maintenance work to a professional company with stiff penalty clauses. It was agreed that if the it was statistically proven that probability of temperature going outside the 2 deg - 4 deg C during the one-year contract was above 2.5% and less than 5% then the penalty would be 10% of AMC (annual maintenance case). In case it it exceeded 5% then the penalty would be 25% of the AMC fee. Problem 2 In Mar 2018, Cold Storage started getting complaints from their Clients that they have been getting complaints from end consumers of the dairy products going sour and often smelling. On getting these complaints, the supervisor pulls out data of last 35 days temperatures. As a safety measure, the Supervisor has been vigilant to maintain the temperature below 3.9 deg C. Assume 3.9 deg C as upper acceptable temperature range and at alpha = 0.1 do you feel that there is need for some corrective action in the Cold Storage Plant or is it that the problem is from procurement side from where Cold Storage is getting the Dairy Products.

1. Project -1 (Cold Storage Case Study)
Saleesh Satheeshchandran

2. Table of Contents
Problem 1
1. Find mean cold storage temperature for Summer, Winter and Rainy
Season
2. Find overall mean for the full year
3. Find Standard Deviation for the full year
4. Assume Normal distribution, what is the probability of temperature
having fallen below 2 degree C?
5. Assume Normal distribution, what is the probability of temperature
having gone above 4 degree C?
6. What will be the penalty for the AMC Company?
Problem 2
1. State the Hypothesis, do the calculation using z test
2. State the Hypothesis, do the calculation using t test
3. Give your inference after doing both the tests

3. Problem 1
1. Find mean cold storage temperature for Summer, Winter and Rainy
Season
Summer – 3.15
Winter – 2.70
Rainy – 3.04
2. Find overall mean for the full year
Overall Mean – 2.96
R Studio – Screen shot

4. 3. Find Standard Deviation for the full year
SD for full year – 0.51
R Studio screenshot

5. 4. Assume Normal distribution, what is the probability of temperature
having fallen below 2 degree C?
Ans. 2.99%
5. Assume Normal distribution, what is the probability of temperature
having gone above 4 degree C?
Ans. 2.07%
6. What will be the penalty for the AMC Company?
Ans. The probability of temperature deviating from 2-4 interval is 5.06%.
As per the contract, if this goes above 5%, the AMC has to pay 25%
penalty.
Excel screenshot
R- screenshot

6. Problem - 2
1. State the Hypothesis, do the calculation using z test
Null Hypothesis (H0) : Temperature of the storage remains less than or
equal to 3.9 degree Celsius
Alternate Hypothesis (H1) : Temperature of the storage goes above 3.9
degree Celsius
Alpha = .1
n = 35
xbar = 3.974
mue0 = 3.9
sigma = 0.51
z=(xbar-mue0)/(sigma/sqrtn) = 0.858411
Pvalue=pnorm(-abs(z)) = 0.1953326
Since Pvalue is greater than Alpha, Null Hypothesis is accepted. Hence, the
temperature of the storage does not go above 3.9 degree Celsius.
R Screenshot

7. 2. State the Hypothesis, do the calculation using t test
Null Hypothesis (H0) : Temperature of the storage remains less than or
equal to 3.9 degree Celsius
Alternate Hypothesis (H1) : Temperature of the storage goes above 3.9
degree Celsius
Alpha = .1
n = 35
xbar = 3.974
mue0 = 3.9
sd = 0.16
tstat=(xbar-mue0)/(sd/sqrtn) = 2.736187
Pvalue1=pt(tstat,34)= 0.9950957
Since Pvalue1 is greater than Alpha, Null Hypothesis is accepted. Hence, the
temperature of the storage does not go above 3.9 degree Celsius.
RStudio Screenshot

8. 3. Give your inference after doing both the tests (10 marks)
We have done a t-test and an z-test to determine if the temperature range of
the storage facility goes above 3.9 degree Celsius in a statistically significant
manner.
In z-test we have calculated the z-value and then the Pvalue. The Pvalue is
more than the alpha (0.1). Hence, we have a 90% confidence in the result.
In t-test we have calculated the tstat value and then the Pvalue. The Pvalue is
more than the alpha (0.1). Hence, we have a 90% confidence in the result.
Since both the tests are confirming the null hypothesis, it can be safely
assumed that the storage facility does not have issue with its functioning.
There might be some issue with the procurement department and the
necessary investigations need to be done.