I. Conduct an investigation considering the following concepts: Null hypothesis Alternative hypothesis Significance level Hypothesis testing Type I error Type II error Test statistic Decision rule...

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I. Conduct an investigation considering the following concepts: Null hypothesis Alternative hypothesis Significance level Hypothesis testing Type I error Type II error Test statistic Decision rule Critical value One-tail test Two-tail test Hypothesis test p-value Guiding questions to answer in writing: Define and distinguish theoretical and statistical objectives for testing a hypothesis. Illustrate with an example When testing a hypothesis, determine whether the observed sampling effects are due to actual differences in population parameters or to sampling error. What two things must be predicted to start a hypothesis test? A null hypothesis is rejected when the value of p is small or large? What is the function of the significance level of a hypothesis test? II. Answer all questions provided about the concepts in Module # 4: Hypothesis Testing, Statistical Inference Steps 1. A restaurant chain states that the customer wait time is 8 minutes with a population standard deviation of 1 minute. The quality control department found in a sample of 50 clients that the average waiting time was 2.75 minutes. With the 0.05 level of significance, can you conclude that the mean waiting time is less than 3 minutes? Demonstrate the procedure and explain your answer. 2. From its experience, an insurance company estimates the average damage from a natural disaster in its area to be $ 35,000. After submitting various loss prevention plans, the company takes a random sample of 200 policyholders and discovers that the median amount per claim was $ 34,800, with a standard deviation of $ 10,300. Were the prevention plans effective in reducing the average number of complaints? Use a significance level of 0.05. 3. Mall owners want to study their customers' shopping habits. Based on previous studies, homeowners are under the impression that a typical shopper spends 0.75 hours at the mall, with a standard deviation of 0.10 hours. Recently, the mall's owners included some specialty restaurants designed for customers to spend more time in it. A consulting firm was hired to evaluate the effects of the restaurants. A sample of 45 customers showed that the average time spent at the mall increased to 0.80 hours. i. Develop a hypothesis test to determine if the mean time spent at the mall is greater than 0.75 hours. Use a significance level of 0.05. ii. Suppose the mean shopping time actually increased from 0.75 to 0.77 hours. What is the probability that this increase will not be detected? iii. When the consultant communicated the information in part ii to the owners, they were upset because a survey did not detect a change from 0.75 to 0.77 hours of shopping time. How can this probability be reduced? Consider the following when submitting your test: • Present your answers with the aspects learned so far about Hypothesis tests, steps of statistical inference. I would really appreciate if this time my homework is 100% plagiarism free as I had problems previously with the homework you did for me as they had 20% plagiarism.