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- Subject Code : STA101A
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- Subject Name : Statistics
Data-Informed Decision-Making
Table of Contents
Executive Summary.
Introduction.
Finding.
Chi-Squared Test.
Hypothesis Testing-I.
Hypothesis Testing-II.
Conclusion.
Recommendation.
References.
Executive Summary of Data-Informed Decision-Making
Data-driven decision making is necessary for all of the organization to retain its business suitably. Organization decide on their future action depending upon the historical data by applying statistical learning and by implicating the relevant strategy. After deciding the fact by getting the statistical outcome, the organization will progress upon this. In this paper, the data-driven decision will be made on the different organization based upon the historical data.
Introduction to Data-Informed Decision-Making
Three tests have been performed on three different organization named KFC, Music company and the Old Brighton Hotel based upon the historical data. The paper aims to determine the hypothesis which will be suitable for their future business and those have been performed by Chi-Squared test, One-tail T-Test and Two-tail T-Test. The analysis and testings are shown in the next section.
Finding of Data-Informed Decision-Making
Chi-Squared Test
This section deals with the Chi-Squared Test. The problem and the hypothesis are concerning to KFC food scenario and the food selling techniques are shown below:
The above table shows the observed values of the foods according to the time slots. Now, according to the observerd values, the hypothesis has been formulated and those are as follows (Klausner, et al., 2016):
Null hypothesis (Ho): There is no relationship between the Time and Type of Food.
Alternative hypothesis (Ha): The time and the type of food are significantly related.
To satisfy the hypothesis, the Chi-Squared test has been conducted. After executing the Chi-Squared test on the observed data, the expected values and the Chi-Squared values are obtained and the values are as follows:
Now, from the Chi-Squared test, the values are obtained through which the Ch-Squared value will be obtained (Cheng, et al., 2019). So, the final Chi-Squared value is obtained by 27.57. After that, the critical Ch-Squared value is obtained by the formula CHIINV(0.05, df). In this case, the degree of freedom is 2 (3-1). The critical chi-squared value is found by 5.99. Now, by comparing the chi-squared value with the critical chi-squared value, the Null Hypothesis will be rejected and the Alternative hypothesis will be accepted as 27.57>5.99 (Miyashita, et al., 2016).
Strategy: As the observation found from the Chi-Squared Test, KFC should focus on the foods that are in demand by time.
Hypothesis Testing-I
In this section, the hypothesis testing has been done on the length of pop music to attract listeners. The hypotheses are considered as:
Null hypothesis (Ho): There is no significant relationship between duration and attractiveness of the pop songs.
Alternative hypothesis (Ha): The Pop songs will be attractive if the duration is of average 3 minutes.
In this context, One-tail T-Test is chosen as the experiment is for the length of the pop songs for the attractiveness to the listeners to be of average 3 min in length. So, the analysis will be made on only one direction using 1 sample (Khanduri, et al., 2019).
Now, by computing the one tail t-test on the given data (50 songs), the t-score is determined by 66.16. Additionally, the critical t-score for the sample with df=49 is 2.01. So, the t-score is greater than the critical t-score (66.16 > 2.01). Thus, the Alternative hypothesis has been satisfied (Zhang, et al., 2019). So, business advice can be made as follows:
Finding: Pop songs should be on average 3 minutes long to attract the listeners.
Advice: To attract listeners, pop songs should be made with an average length of 3 minutes or 180m seconds.
Hypothesis Testing-II
In this section, the selling of the beer at Old Brighton Hotel will be analysed based on the availability of salted peanut on the table to increase the sell. The hypotheses are as follows:
Null hypothesis (Ho): There is no relationship between the selling of beer with the presence of salted peanuts.
Alternative hypothesis (Ha): If the salted peanut will be on the table, the sell of beer will be higher.
The data contains two variable named Salted peanuts and No peanuts. The analysis has been conducted in both of the direction to check the effect of the salted peanut on the table for two slots each of which contains 60 random nights. So, in this context, to satisfy the outcome by checking the effect on both of the directions, Two-tailed and two-sample t-test has been conducted (Bar & Tabrikian, 2018). The calculation of the t-test is shown as follows:
From the analysis, the t-value is obtained as 0.67 and the critical value of t-statistics is 1.66. As the critical value of t-statistics is greater than the calculated t-statistics, so, the Null Hypothesis will be accepted (Khanduri, et al., 2019). So, the business advice to Old Brighton hotel is as follows:
Advice & Finding: Old Brighton Hotel should have seen the selling of the beer is not dependent upon the salted peanut. So, they can cut down the additional cost of peanut having on the table.
Conclusion on Data-informed Decision-Making
The statistical tests have been performed and the hypotheses have been focused accordingly. In the subsections of the finding, the relevant finding and the business strategies are mentioned which will be suitable for the future business.
Recommendation on Data-informed Decision-Making
In this paper, three tests have been performed and the recommendations are given as follows:
- The Chicken Pieces and Wraps are observed to be highly deviated for the Expected value and compared to the original value. But, the less deviation in the expected values is observed for Burger (From Chi-Squared test).
- To attract listeners, pop songs should be made with an average length of 3 minutes or 180m seconds (From Hypothesis testing-I).
- Old Brighton Hotel should have seen the selling of the beer is not dependent upon the salted peanut. So, they can cut down the additional cost of peanut having on the table (From Hypothesis testing-II).
References for Data-informed Decision-Making
Bar, S. & Tabrikian, J., 2018. A Sequential Framework for Composite Hypothesis Testing. IEEE Transactions on Signal Processing, 66(20), pp. 5484 - 5499.
Cheng, J., Sun, X., Liu, P. & Mou, H., 2019. An Improved Residual Chi-Square Test Fault Isolation Approach in Four-Gyro SINS. IEEE Access, Volume 7, pp. 174400 - 174411.
Khanduri, P., Pastor, D., Sharma, V. & Varshney, P. K., 2019. Truncated Sequential Non-Parametric Hypothesis Testing Based on Random Distortion Testing. IEEE Transactions on Signal Processing, 67(5), pp. 4027 - 4042.
Klausner, N., Azimi-Sadjadi, M. R. & Scharf, L. L., 2016. Saddlepoint Approximations for Correlation Testing Among Multiple Gaussian Random Vectors. IEEE Signal Processing Letters, 23(5), pp. 703 - 707.
Miyashita, Y., Ideguchi, S. & Takahashi, K., 2016. Performance test of RM CLEAN and its evaluation with chi-square value. Publications of the Astronomical Society of Japan, 68(3), pp. 44 - 44.
Zhang, S., Khanduri, P. & Varshney, P. K., 2019. Distributed Sequential Detection: Dependent Observations and Imperfect Communication. IEEE Transactions on Signal Processing, pp. 830 - 842.
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