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AET 703 Technology Management Analytics

Student’s Name:

Project Description

French Fried Potato Manufacture

Date: March 8, 2022

Scenario.

The purpose of the project is being worker in major food manufacturer (Lambda Foods) to analyze the raw data regarding Potatoes size. The target size of the potato is 10 ounces plus or minus one-half of an ounce. In the containerizing process culls are removed bringing uniformity into the containers’ contents.

Sample

To pick the three samples of 25 potatoes each. I used the simple random sampling, this sampling technique gives each member of the population an equal chance of being chosen. It is not a haphazard sample as some people think! One way of achieving a simple random sample is to number each element in the sampling frame (e.g. give everyone on the Electoral register a number) and then use random numbers to select the required sample.

Normality test: normality is the pattern of thoughts, feelings or behaviour that confirms to a usual, typical or expected standard. I run the Kolmogorov-Smirnov and Shapiro-Wilk tests to check the normality of the samples

Case Processing Summary
	Cases
	Valid	Missing	Total
	N	Percent	N	Percent	N	Percent
Sample 1	25	100.0%	0	0.0%	25	100.0%
Sample 2	25	100.0%	0	0.0%	25	100.0%
Sample 3	25	100.0%	0	0.0%	25	100.0%

Shapiro wilk test is used to test whether random sample coming from normal distribution or not. While dealing with very small sample, you will be cautious while interpreting Shapiro wilk test because power of test is also small. If deviation in the data is small then denominator become small and we get larger value of w. So we can conclude that sample is drawn from normal distribution which may lead to wrong interpretation.

Tests of Normality
	Kolmogorov-Smirnova	Shapiro-Wilk
	Statistic	df	Sig.	Statistic	df	Sig.
Sample 1	.089	25	.200*	.979	25	.855
Sample 2	.174	25	.050	.934	25	.106
Sample 3	.087	25	.200*	.973	25	.713
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction

The tests and graphs are clearly shows that none of the sample is normally distributed.

Data Mean and Standard Deviation

Sample 1	Mean	9.9868	0.0180621
	95% Confidence Interval for Mean	Lower Bound	9.949522
		Upper Bound	10.02408
	5% Trimmed Mean	9.985
	Median	9.99
	Variance	0.008
	Std. Deviation	0.090311
	Minimum	9.82
	Maximum	10.2
	Range	0.38
	Interquartile Range	0.105
	Skewness	0.205	0.464
	Kurtosis	0.394	0.902
Sample 2	Mean	9.9764	0.0318532
	95% Confidence Interval for Mean	Lower Bound	9.910658
		Upper Bound	10.04214
	5% Trimmed Mean	9.982667
	Median	9.99
	Variance	0.025
	Std. Deviation	0.159266
	Minimum	9.59
	Maximum	10.26
	Range	0.67
	Interquartile Range	0.17
	Skewness	-0.817	0.464
	Kurtosis	1.222	0.902
Sample 3	Mean	9.9792	0.035435
	95% Confidence Interval for Mean	Lower Bound	9.906066
		Upper Bound	10.05233
	5% Trimmed Mean	9.986778
	Median	9.98
	Variance	0.031
	Std. Deviation	0.177175
	Minimum	9.52
	Maximum	10.27
	Range	0.75
	Interquartile Range	0.24
	Skewness	-0.502	0.464
	Kurtosis	0.515	0.902

Interpretation:

Sample 1. The average size is 9.9868 ounces and we are 95% confident that the average size of the population is in between 9.949522 and 10.0240.

Sample 2. The average size is 9.910658 ounces and we are 95% confident that the average size of the population is in between 10.04214 and 9.982667

Sample 3. The average size is 9.9792 ounces and we are 95% confident that the average size of the population is in between 9.906066 and 10.05233. The detail descriptive summary is give in the above table.

Meeting Target Size.

Hypothesis testing is a demonstration of insights, statistics by which an expert tests a presumption in regards to a populace boundary. The strategy utilized by the investigator relies upon the idea of the information utilized and the justification behind the examination. Hypothesis testing is utilized to evaluate the believability of a theory by utilizing test information. Such information might come from a bigger populace, or from the information creating process.

The alpha equal 0.05 significance level.

Decision Rule: Reject the null hypothesis if the p value is less than 0.05.

Hypothesis testing one (Sample 1)

Null hypothesis Ho: the average size of the potato is less than or equal to 9.8 ounces

Ho: µ ≤ 9.8

Alternative hypothesis Ha: the average size of the potato is higher than 9.8 ounces

Ha: µ > 9.8

Test Output:

Sample 1:

One-Sample Statistics
	N	Mean	Std. Deviation	Std. Error Mean
Sample 1	25	9.986800	.0903106	.0180621

One-Sample Test
	Test Value = 9.8
	t	df	Sig. (2-tailed)	Mean Difference	95% Confidence Interval of the Difference
					Lower	Upper
Sample 1	10.342	24	.000	.1868000	.149522	.224078

The p value (0.000) is less than 0.05 hence we reject the null hypothesis and concluded the average size of the potato is higher than 9.8 ounces

Hypothesis testing two (Sample 2)

Null hypothesis Ho: the average size of the potato is less than or equal to 10 ounces

Ho: µ ≤ 10

Alternative hypothesis Ha: the average size of the potato is higher than 10 ounces

Ha: µ > 1o

Test Output:

Sample 2:

One-Sample Statistics
	N	Mean	Std. Deviation	Std. Error Mean
Sample 2	25	9.976400	.1592660	.0318532

One-Sample Test
	Test Value = 10
	t	df	Sig. (2-tailed)	Mean Difference	95% Confidence Interval of the Difference
					Lower	Upper
Sample 2	-.741	24	.466	-.0236000	-.089342	.042142

The p value (0.466) is higher than 0.05 hence we fail to reject the null hypothesis and concluded the average size of the potato is not higher than 9.8 ounces

Hypothesis testing three (Sample 3)

Null hypothesis Ho: the average size of the potato is less than or equal to 9.5 ounces

Ho: µ ≤ 9.5

Alternative hypothesis Ha: the average size of the potato is higher than 10 ounces

Ha: µ > 9.5

Test Output:

Sample 3:

One-Sample Statistics
	N	Mean	Std. Deviation	Std. Error Mean
Sample 3	25	9.979200	.1771751	.0354350

One-Sample Test
	Test Value = 9.5
	t	df	Sig. (2-tailed)	Mean Difference	95% Confidence Interval of the Difference
					Lower	Upper
Sample 3	13.523	24	.000	.4792000	.406066	.552334

The p value (0.000) is less than 0.05 hence we reject the null hypothesis and concluded the average size of the potato is higher than 9.5 ounces

Forecasting Capacity Needs

The factory has seasonal demand for the finished product. For the last 20 quarters the data which seems to support this seasonality. These numbers represent millions of pounds of potatoes.

Based on the historical data the regression forecast model is:

Y=1.184-0.012*x

Slope	-0.012
Intercept	1.184

Y represent the predicted forecast value while represent the time.

The detail table is shown below.

Potato Demand

Year	Time (Period)	Potato Demand (millions) (Actual)	Forecast	Act-Forecast (Error)	Abs(A-F) (Error)	Error^2	Percent Error
2017	1	1.03	1.1721	-0.1421	0.1421	0.0202	13.80%
	2	0.89	1.1601	-0.2701	0.2701	0.0729	30.35%
	3	1.24	1.1480	0.0920	0.0920	0.0085	7.42%
	4	1.5	1.1359	0.3641	0.3641	0.1325	24.27%
2018	5	0.95	1.1239	-0.1739	0.1739	0.0302	18.30%
	6	1.02	1.1118	-0.0918	0.0918	0.0084	9.00%
	7	1.36	1.0997	0.2603	0.2603	0.0677	19.14%
	8	1.11	1.0877	0.0223	0.0223	0.0005	2.01%
2019	9	0.89	1.0756	-0.1856	0.1856	0.0344	20.85%
	10	1.05	1.0635	-0.0135	0.0135	0.0002	1.29%
	11	1.29	1.0515	0.2385	0.2385	0.0569	18.49%
	12	1.34	1.0394	0.3006	0.3006	0.0904	22.43%
2020	13	0.89	1.0273	-0.1373	0.1373	0.0189	15.43%
	14	0.76	1.0153	-0.2553	0.2553	0.0652	33.59%
	15	1.29	1.0032	0.2868	0.2868	0.0823	22.23%
	16	1.04	0.9911	0.0489	0.0489	0.0024	4.70%
2021	17	0.8	0.9791	-0.1791	0.1791	0.0321	22.38%
	18	0.57	0.9670	-0.3970	0.3970	0.1576	69.65%
	19	1.19	0.9549	0.2351	0.2351	0.0553	19.75%
	20	0.94	0.9429	-0.0029	0.0029	0.0000	0.30%

Average Error	0.0000
MSE	0.0325
MAD	0.1478
MAPE	15.48%

Mean Absolute Deviation=0.1478, Mean Absolute Percentage Error=15.48% and Mean Squared Error=0.0325

All three of them are indicators of forecasting accuracy wherein forecasts have been made over a period of time. However, the parameters used to determine the forecasting accuracy vary and thus above three methods.

MAD takes into consideration absolute values of forecasting errors and average them over entire forecasting period. Forecasting error for a specific time period means difference between actual parameter and forecasted parameter. It must be noted that only Absolute Values are taken which always ensures that set of data are positive which when averaged gives Mean Absolute Deviation.

MAPE is further refinement on MAD. Here instead of absolute deviation, Absolute Percentage Error is used. Absolute Percentage Error equals Absolute deviation divided by Actual data and multiplied by 100. Otherwise approach for calculating MAPE is same as MAD

MSE is calculated by squaring all errors and dividing it by "n - 1" "n" stands for number of data. It must be noted that Mean under MAD or MAPE is arrived by dividing numerator with "n", whereas MSE is calculated by dividing numerator with "n - 1".

Summary.

Three samples are picked from the data populations each one has 25 observations and all the three samples are not normally distributed. Similarly the sample 1 and sample 3 data means support the alternative hypothesis and sample 2 support null hypothesis at 5% level of significances.

The equation for the forecast is

Y=1.184-0.012*x

Y represent the predicted forecast value while represent the time.

The predicted value for 2022 using above regression equation:

	Time (Period)	Forecast
2022	21 Q1	0.931
	22 Q2	0.919
	23 Q3	0.907
	24 Q4	0.895

References

Bordalo, P. G. (2020). Overreaction in macroeconomic expectations. . American Economic Review, 110(9), 2748-82.

Jugend, D. F. (2020). Public support for innovation: A systematic review of the literature and implications for open innovation. Technological Forecasting and Social Change, 15(6), 119-185.

Ma, Y. R. (2019). Oil financialization and volatility forecast: Evidence from multidimensional predictors. Journal of Forecasting, 38(6), 564-581.

Denis, D. J. (2018). SPSS data analysis for univariate, bivariate, and multivariate statistics. John Wiley & Sons.