This paper aims to test the module ILOs using a practical real-life case-study. In this case study, you are going to play the role of an analyst for one of the corporates, let us call it Company-Z. Therefore, let us first introduce the case-study random variables: Y1 is the Company-Z monthly revenue along the period Pre-COVID-19 (January 2018 to December 2019); Y2 is the same Company-Z monthly revenue but during the period Post-COVID-19 (March 2020 to September 2020); X1 is the monthly operations cost during the period Pre-COVID-19 (January 2018 to December 2019); while X2 is the same monthly operations cost but during the period Post-COVID-19 (March 2020 to September 2020). Accordingly, in your analysis, you will depend on two main random variables over two time series. The first random variable is the Company-Z monthly revenue Y, and the second random variable is the Company-Z monthly operations cost X. The two random variables were chosen over two periods of time: the first is (Pre-COVID-19: January 2018 to December 2019), and the second is (Post-COVID-19: March 2020 to September 2020). Your task is to prepare a comprehensive report to the company, fulfilling specific requirements outlined below in point

1. What are the 95 percent confidence intervals for the average monthly operations cost Pre- and Post- COVID-19 X1& X2? And what do you conclude by comparing these intervals? Moreover, what is the used methodology of constructing the confidence interval for each random variable, and why did you use the proposed methodology for each random variable?

use the confidence level 95 percen

Date Pre-COVID-19 Pre-COVID-20 Date2 Y1 (L.E.) X1 (L.E.) Post-COVID-19 Y2 X2 (L.E.) (L.E.) 2941.6 11.0 2952.1 8.1 3.8 6.6 3933.3 3931.7 3934.3 3930.4 3931.7 3.8 2949.3 7.0 8.3 Mar/2020 Apr/2020 May/2020 Jun/2020 Jul/2020 Aug/2020 Sep/2020 2947.4 11.2 6.0 2946.9 8.3 6.2 2944.6 2950.4 13.2 8.2 3932.4 3931.5 3933.6 3932.3 3934.3 3932.0 3932.2 7.0 5.7 6.2 4.0 5.9 6.2 Jan/2018 Feb/2018 Mar/2018 Apr/2018 May/2018 Jun/2018 Jul/2018 Aug/2018 Sep/2018 Oct/2018 Nov/2018 Dec/2018 Jan/2019 Feb/2019 Mar/2019 Apr/2019 May/2019 Jun/2019 Jul/2019 Aug/2019 Sep/2019 Oct/2019 Nov/2019 Dec/2019 5.4 4.1 3930.5 3934.0 3933.3 3933.8 3934.9 4.0 4.1 4.6 3933.4 5.2 3930.9 6.1 7.3 3931.1 3933.9 3933.0 3.3 6.2 5.9 3931.5 3933.5 3.7 Date Pre-COVID-19 Pre-COVID-20 Date2 Y1 (L.E.) X1 (L.E.) Post-COVID-19 Y2 X2 (L.E.) (L.E.) 2941.6 11.0 2952.1 8.1 3.8 6.6 3933.3 3931.7 3934.3 3930.4 3931.7 3.8 2949.3 7.0 8.3 Mar/2020 Apr/2020 May/2020 Jun/2020 Jul/2020 Aug/2020 Sep/2020 2947.4 11.2 6.0 2946.9 8.3 6.2 2944.6 2950.4 13.2 8.2 3932.4 3931.5 3933.6 3932.3 3934.3 3932.0 3932.2 7.0 5.7 6.2 4.0 5.9 6.2 Jan/2018 Feb/2018 Mar/2018 Apr/2018 May/2018 Jun/2018 Jul/2018 Aug/2018 Sep/2018 Oct/2018 Nov/2018 Dec/2018 Jan/2019 Feb/2019 Mar/2019 Apr/2019 May/2019 Jun/2019 Jul/2019 Aug/2019 Sep/2019 Oct/2019 Nov/2019 Dec/2019 5.4 4.1 3930.5 3934.0 3933.3 3933.8 3934.9 4.0 4.1 4.6 3933.4 5.2 3930.9 6.1 7.3 3931.1 3933.9 3933.0 3.3 6.2 5.9 3931.5 3933.5 3.7