Project Three - 30 points The purpose of the project is to give you an opportunity to work on a data analysis using StatCrunch. In this project, you will do inference for a mean to solve a problem in the real world using t- interval and test learned from chapter 10 (Paik's note). The below link is for student tutorial videos for StatCrunch that are posted on YouTube. StatCrunch Tutorials: https://www.youtube.com/view_play_list?p=BE055F65E43B4973 The below link is for the Student help section of StatCrunch http://www.statcrunch.com/app/help.php Mercedes Madness A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon-to-1:00 p.m. lunch period. The waiting time (defined as the time the customer enters the line until he or she reaches the teller window) of 16 customers randomly selected during this hour is recorded over a period of 1 week. A random sample of 16 customers is selected. The data are saved in a file called Time.csv, which can be found at Projects menu in Blackboard. To load this data with Statcrunch, Download \"Time.csv\" from our blackboard homepage to your computer. Access https://www.statcrunch.com/ with your Mystatlab ID Click File menu and Choose \"Time.csv\" in your computer Click Load File. 1. Using Statcrunch, create a histogram of the data with summary statistics. Report the values of the sample mean and the sample standard deviation for these data. In addition, identify the population and parameter of interest. Print histogram with summary statistics. 2. Do these data satisfy the assumptions for inference (CI or Test)? Use a histogram and normal probability plot. If not, what assumptions must you make in order to use these data for inference? Print a normal probability plot. To make a normal probability plot: Click on Graph Choose QQ plot Choose the variable Column Click Compute 3. Using Statcrunch, construct a 90% confidence interval for the population mean of waiting time. To construct a confidence interval: Click on Stat Choose T statistics One sample with data Choose the variable Column 1 Indicate Confidence Interval for , and then enter the Level of confidence Click Compute Comment: L.limit and U.limit corresponds confidence interval. 4. Give an interpretation for the 90% confidence interval you calculated. 5. Based on your confidence interval, is there evidence that the population mean waiting time is less than 6 minutes? 6. You want to check if there evidence that the population mean waiting time is less than 6 minutes by using a hypothesis test with = 0.01? To do t-test: Click on Stat Choose T statistics One sample with data Choose the variable Column Indicate Hypothesis Test, then enter the hypothesized Null mean, and choose the Alternative hypothesis Click Compute. Comment: The population standard deviation is unknown in this problem, we have to estimate it using the sample standard deviation s. Using s instead of adds more uncertainty x . This additional variability and hence variability to the distribution of the test statistic s/ n can be accounted for by using the t-distribution for finding the p-value as it has heavier tails than the standard normal distribution. Based on the Statcrunch output, answer the following questions: (a) State the hypotheses. (b) Find the test statistic. (c) Find the p-value. (d) Provide an interpretation of the p-value within the context of the problem. (e) Based on the p-value and the level of significance make a decision about H0 . (f) Based on the decision write a conclusion in terms of the problem. 2