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In: Operations Management

Calculate the average daily inventory holding cost during Pre- and Post- COVID-19 X1& X2? Explain whether...

Calculate the average daily inventory holding cost during Pre- and Post- COVID-19 X1& X2? Explain whether this average is considered as population parameters or sample statistics? Justify your answer? [15 marks]
What is the 95 percent confidence intervals for the average daily inventory holding cost Pre- and Post- COVID-19 X1& X2? And what do you conclude by comparing these intervals? Also what is the 99 percent confidence interval for the average daily inventory holding cost Post- COVID-19 X2? And what do you conclude by comparing the 95 and 99 percent confidence intervals for the average daily inventory holding cost Post- COVID-19 X2? [15 Marks]
Suppose there is a hypothesis arguing that the population mean of the daily inventory holding cost is 1.5 times the value of average daily inventory holding cost during the selected period (November and December 2019) Pre-COVID-19 X1. List the full analytical steps to test this hypothesis? Comment on the result and write your conclusion regarding the hypothesis? [15 marks]
To what extent is there a change in the pattern or the power of the relationship Pre- and Post- COVID-19 between the daily inventory holding cost X and the daily sales Y? Support your answer with the appropriate statistical evidences. [15 marks]

Discuss the appropriate statistical technique that can explain the variation in the daily sales because of the daily inventory holding cost Post-COVID-19 post COVID 19. Justify your answer.

Solutions

Expert Solution

Answer a :

Date	Pre-COVID-19	Date	Post-COVID-19
	Y1	X1		Y2	X2
01-Nov-19	4365.5	7	01-Apr-20	3612.2	11.9
02-Nov-19	4365.8	7.1	02-Apr-20	3617	8.6
03-Nov-19	4366.3	7.2	03-Apr-20	3614.9	7.9
04-Nov-19	4365.9	7.7	04-Apr-20	3612.3	11.4
05-Nov-19	4365.7	7.3	05-Apr-20	3617.5	8.1

	Average	7.26			9.58

The average daily inventory holding cost during Pre- COVID-19 is 7.26

The average daily inventory holding cost during Post- COVID-19 is 9.58.

Parameter: Mathematically summarization and description of collections of population data.

Statistic: Mathematically summarization and description of collections of sample data.

These means are the sample statistics because the data is for only 5 days each.

Answer b :

95% Confidence interval for X1

Sample mean of X1 is

Sample standard deviation of X1 is

Degree of freedom = 5-1 = 4

From t-table, for 95% confidence value and degree of freedom =4,

t = 2.776

The 95% Confidence interval is calculated as:

The 95% confidence interval for average daily inventory holding cost Pre- Covid-19 is (6.60, 9.48)

95% Confidence interval for X2

Sample mean of X2 is

Sample standard deviation of X1 is

Degree of freedom = 5-1 = 4

From t-table, for 95% confidence value and degree of freedom =4,

t = 2.776

The 95% Confidence interval is calculated as:

The 95% confidence interval for average daily inventory holding cost Post- Covid-19 is (8.23, 11.97)

Comparing the 95% confidence interval for average daily inventory holding cost for Pre and Post- Covid-19, we see that there is a small overlap in the confidence interval regions of both values. Thus there isn't convincing evidence that average inventory cost for Pre and Post Covid-19 are different.

99 percent confidence interval for tX2

Degree of freedom = 5-1 = 4

From t-table, for 99% confidence value and degree of freedom =4,

t = 4.602

The 99% Confidence interval is calculated as:

The 99% confidence interval for average daily inventory holding cost Post- Covid-19 is (7.00, 14.01)

The 95% confidence interval for X2 is (8.23, 11.97), while the 99% confidence interval is (7.00, 14.01). We can be 95% confidence that the average daily inventory holding cost Post- Covid-19 lies between 8.23 and 11.97 while we can be 99% confidence that the average daily inventory holding cost Post- Covid-19 lies between 7.00 and 14.01.

Comparing both the confidence intervals we conclude that, the 99% confidence interval is significantly wider than the 95% confidence interval.

Answer c :

For computation of mean and sample standard deviation, S of X1 in excel follow the given steps:

Firstly enter the data into excel
Then for mean, use the function '=AVERAGE(data)' where in data select X1 dataset.
Then for S, use funtion '=STDEV.S(data)' where in data select X1 dataset.

Answer d :

The data set

Pre-COVID-19		Post-COVID-19
Date	Sales (Y1)	Inventory (X1)	Date	Sales (Y1)	Inventory (X1)
01 November 2019	3226.7	8.5	01 April 2020	1714.4	13.1
02 November 2019	3224.4	8.2	02 April 2020	1720.3	9.8
03 November 2019	3228.1	7.3	03 April 2020	1710.7	13.6
04 November 2019	3226.2	8	04 April 2020	1711.1	14.3
05 November 2019	3226.6	8	05 April 2020	1709.6	14.3
06 November 2019	3226.7	7.9	06 April 2020	1710.3	14.7
07 November 2019	3226.8	7.6	07 April 2020	1702.6	17.8
08 November 2019	3223.7	8.4	08 April 2020	1718.4	11.1
09 November 2019	3225	8.4	09 April 2020	1712.3	10.8
10 November 2019	3222.5	8.3	10 April 2020	1713.8	11.7
11 November 2019	3223.8	7.9	11 April 2020	1718.5	7.3
12 November 2019	3226.9	7.7	12 April 2020	1717.6	11
13 November 2019	3224.9	8	13 April 2020	1710.5	15.3
14 November 2019	3230.1	7.8	14 April 2020	1713.3	14
15 November 2019	3225.6	7.9	15 April 2020	1713.5	11
16 November 2019	3225.1	7.7	16 April 2020	1715.1	10.9
17 November 2019	3225.7	7.8	17 April 2020	1718	10.3
18 November 2019	3224.4	8.4	18 April 2020	1717.5	10.9
19 November 2019	3224.9	7.8	19 April 2020	1716.1	9.7
20 November 2019	3226.3	7.7	20 April 2020	1715.4	12.2
21 November 2019	3228.1	7.4	21 April 2020	1715.8	11.2
22 November 2019	3225.7	8.1	22 April 2020	1709	13.7
23 November 2019	3224.4	8.2	23 April 2020	1710.8	13.2
24 November 2019	3225.8	8.1	24 April 2020	1714.5	10.5
25 November 2019	3225.7	7.9	25 April 2020	1714.4	12
26 November 2019	3227.3	8.2	26 April 2020	1715.4	12.7
27 November 2019	3226.2	7.8	27 April 2020	1717.9	10.2
28 November 2019	3225.6	8.4	28 April 2020	1716.2	12.3
29 November 2019	3226.8	7.9	29 April 2020	1716.5	11.6
30 November 2019	3224.4	8.1	30 April 2020	1711.6	15.3
01 December 2019	3228.5	7.7	01 May 2020	1717.5	11.8
02 December 2019	3227	7.9	02 May 2020	1721.6	6.4
03 December 2019	3224.5	8	03 May 2020	1713.2	12.4
04 December 2019	3225	8	04 May 2020	1713.9	12.8
05 December 2019	3227.7	7.9	05 May 2020	1709.1	14.4
06 December 2019	3228.6	7.8	06 May 2020	1721.2	9.5
07 December 2019	3228.4	7.5	07 May 2020	1720.1	9.6
08 December 2019	3227	7.9	08 May 2020	1713.9	9.5
09 December 2019	3227	8.1	09 May 2020	1712.7	12
10 December 2019	3227.6	7.6	10 May 2020	1722.3	8.6
11 December 2019	3226.8	7.6	11 May 2020	1719.7	11.1
12 December 2019	3229	7.7	12 May 2020	1713.9	14.4
13 December 2019	3224	7.9	13 May 2020	1711.8	12.8
14 December 2019	3223.6	8	14 May 2020	1719	8
15 December 2019	3228	7.6	15 May 2020	1720.8	9.9
16 December 2019	3226.1	8.1	16 May 2020	1715.8	13.7
17 December 2019	3226.5	8	17 May 2020	1717.4	8.1
18 December 2019	3229.2	7.6	18 May 2020	1716	11
19 December 2019	3223.5	8.7	19 May 2020	1710.9	14.8
20 December 2019	3227.3	7.8	20 May 2020	1716.7	10.2
21 December 2019	3225.5	7.8	21 May 2020	1716.4	11
22 December 2019	3229.1	7.7	22 May 2020	1715.6	11.2
23 December 2019	3225.6	8.3	23 May 2020	1716.6	12.6
24 December 2019	3224.2	8.2	24 May 2020	1714.6	11.7
25 December 2019	3226.5	8.1	25 May 2020	1719.1	10.5
26 December 2019	3225.4	8.1	26 May 2020	1716	10.1
27 December 2019	3224.1	8.4	27 May 2020	1713.4	12.9
28 December 2019	3227.8	7.6	28 May 2020	1719.2	10.7
29 December 2019	3226.7	7.9	29 May 2020	1718.5	8
30 December 2019	3228.5	7.6	30 May 2020	1717.4	10.2
31 December 2019	3225.4	7.8	31 May 2020	1720.9	10.1

The analysis

Pre-COVID-19		Post-COVID-19

Correlation Co-efficient		Correlation Co-efficient
	Sales (Y1)			Sales (Y1)
Inventory (X1)	-0.647017976		Inventory (X1)	-0.827745401

Covariance		Covariance
	Sales (Y1)			Sales (Y1)
Inventory (X1)	-0.302652513		Inventory (X1)	-6.605834453

From the above analysis we can conclude there is an increase in the stock holding compared to sales in post COVID-19 situation compared to pre COVID-19 situation.

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