answer all questions- In this assignment, you will explore hypothesis testing and its application in the Supply Chain context. Supply chain operations and logistics play a crucial role in the efficient and effective movement of goods, services, and information from suppliers to customers. It involves numerous interconnected processes, such as procurement, inventory management, transportation, and warehousing, all aimed at meeting customer demands while minimizing costs and lead times. To enhance decision-making in supply chain management, hypothesis testing provides a robust statistical framework to evaluate and validate various hypotheses related to important parameters and performance metrics.

Question 1 - Hypothesis test for the population mean when is known

A company claims that their average delivery time for orders is 3.5 days. However, a supply chain analyst believes that the company's average delivery time differs from this claim. To investigate further, the analyst decides to randomly collect the delivery time of 1000 orders and conduct a hypothesis test on the population mean delivery time. The analyst calculates the sample mean and standard deviation of delivery times. The mean is 3.3 and the standard deviation is 1.2 days.

1. Specify the hypotheses in order to test the analysts claim.
2. What is the allowed probability of a Type I error?
3. Calculate the value of the test statistic and the p-value.
4. At the 5% significance level, does average delivery time differ from 3.5?

Question 2 - Hypothesis test for the population mean when is unknown

The same companys CIO claims that their average customer satisfaction rating is above 4.6 out of 5. However, the companys board of directors believes that the company's average customer satisfaction rating is less than 4.6. To investigate further, they hired an analyst to conduct a hypothesis test on the population mean customer satisfaction rating. The analyst does not have information about the population standard deviation. The analyst decides to collect customers satisfaction rating by randomly sending out an online survey to the customers and measure their satisfaction. The analyst calculates the sample mean satisfaction rating. The mean is 4.53.

1. Specify the hypotheses to test.
2. Calculate the value of the test statistic and the p-value.
3. At the 5% significance level, what is the conclusion to the hypothesis test?

Question 3 - Hypothesis test for the population proportion

The company also claims that 73% of its water bottles meet the required quality standards. However, a quality control analyst believes that the company's proportion of products meeting the quality standards differs from this claim. To investigate further, the analyst decides to conduct a hypothesis test on the population proportion of products meeting the quality standards. To do that the analyst randomly selects 500 water bottles and run a test on their quality. The results show that 361 of them pass the quality test.

1. Specify the hypotheses in order to test the analysts claim.
2. Calculate the value of the test statistic and the p-value.
3. At the 5% significance level, what is the conclusion to the hypothesis test?