1. Show ALL Steps including formulas used and all calculations done to arrive at the final answers. Incomplete solutions will receive partial credit.;2. Answer all questions in the context of the problem. General answers are not expected.;3. Use at least FOUR SIGNIFICANT digits at all intermediate steps. Round off the final answers appropriately. Note: 0.0042 is only two significant digits as leading zeros are not considered significant. Trailing zeros are considered significant.;4. Questions are welcome. If your question relates to the solution of a problem, it may not be answered by the instructor.;Final Exam;Points Earned;True or False;Multiple Choice;Problem 1;Problem 2;Problem 3;Problem 4;Total;The Honor Pledge;On my honor, I have neither given nor received unauthorized aid on this examination.;Good Luck!;Student Name (Signature);True or False. (2 points ? 5 = 10 points);Write T or F in the parentheses in the front of each question.;1. () The Central Limit Theorem states that the sampling distribution of sample means will always follow a normal distribution regardless of sample size. True False;2. () In hypothesis testing, the Null hypothesis represents what we want to prove wrong. True False;3. () In regression analysis, we prefer bigger coefficient of determination (). True False;4. () Any sampling methods will guarantee representation of the population as long as there is some randomness involved. True False;5. () In hypothesis testing for population mean, the test statistics we choose depends on whether or not we know the population standard deviation. A statistic should be chosen if we DO know the population standard deviation. True False;Multiple Choice. (2 Points ? 5 = 10 Points);Circle the most appropriate answer clearly.;A manager of a car dealership believes that there is a relationship between the number of salespeople on duty and the number of cars sold. Suppose the following sample is used to develop a simple regression model to predict the number of cars sold by the number of salespeople.;Number of Salespeople;();Number of Cars Sold;();6;79;3.24;655.36;46.08;6;64;3.24;112.36;19.08;4;49;0.04;19.36;0.88;2;23;4.84;924.16;66.88;3;52;1.44;1.96;1.68;12.8;1713.2;134.6;Answer Questions 1-5 based on the above problem statement.;1. () What is the standard deviation of the Number of Salespeople (X)?;A. 4.2 B. 12.8 C. 1.789 D. 1.6;2. () What is the slope of the regression line?;A. 12.71 B. 133.8 C. 32.08 D. 10.52;3. () Estimate the number of cars sold () when the number of salespeople (X) is 5?;A. 50.2 B. 61.8 C. 58.3 D. 60.5;4. () Choose the right formula to construct a 95% confidence interval for the number of cars sold () when the number of salespeople (X) is 5?;A. B.;C. D.;5. () Find the coefficient of determination for this simple regression model?;A. 0.7854 B. 0.8265 C. 0.8812 D. 0.9020;Problem 1. (20 points);The amount of time a bank teller spends with each customer has a population mean minutes and population standard deviation minute.;a) If a customer is randomly selected, what is the probability that the service time would exceed 3 minutes?;b) If many samples of 64 were selected, what are mean and standard error of the mean (standard deviation of the sample means) expected to be? What is the expected shape of the distribution of sample means? Justify your answer.;c) If a random sample of 64 customers is selected, what is the probability that mean service time would exceed 3 minutes?;Problem 2. (20 points);The customer service department of a local gas utility company would like to estimate the average length of time between the entry of service request and the connection of service called the response time. A random sample of 5 houses was selected from the records available during the past year. The results in number of days are displayed below;11, 12, 9, 10, 13;a) Compute the sample mean and sample standard deviation of the response time.;b) Construct a 95% confidence interval for the average response time for all customers requesting connection of service.;c) How would you explain the confidence interval for the response time to the President of the company? Provide a clear and complete answer. Use actual variable names and numbers in your answer. Do not use words like ?population? in your answer that the president may not understand.;Problem 3. (20 points);In an attempt to determine whether or not special training increases the speed with which assembly line workers can do an assembly job at AMTEL Inc., 25 workers are timed performing the task. Then, they are given a special training course designed to increases their assembly efficiency. At the end of the course, they are timed doing the same task. The differences between the first and the second time are recorded for each of the 25 assembly line workers. The mean improvement for the 25 workers was found to be 2.6 minutes and the sample standard deviation was 4 minutes.;Let variable represents the improvement in time for each assembly line worker. Let represents the average improvement in time for the population. Has the training improved the time required on the job? Please test the hypothesis use as the level of significance. (Hint: meaning that the training improves the time. Please follow the 7 step procedure!);Problem 4. (20 points);Consider the following time series data representing quarterly sales of dishwashers at Big Boys Appliances over the past two years;Time;Sales;2010 Quarter 1;25;2010 Quarter 2;85;2010 Quarter 3;64;2010 Quarter 4;30;2011 Quarter 1;70;2011 Quarter 2;125;2011 Quarter 3;105;2011 Quarter 4;90;The scatter plot of the data above shows seasonality with trend. Hence, a multiple regression model is run to forecast the demand. We denote sales (Y) as the depend variable, and denote time (t, with represent the first quarter of 2010) and dummy variables (,, and) as independent variables. Here, we choose quarter 1 as the baseline and adopt three seasonality dummy variables, such that represents quarter 2, represents quarter 3, and represents quarter 4. Answer the following questions. Use;a) (5 points) Use the above variable definition to code the data above.;Time;Sales(Y);Time (t);2010 Quarter 1;25;1;2010 Quarter 2;85;2;2010 Quarter 3;64;3;2010 Quarter 4;30;4;2011 Quarter 1;70;5;2011 Quarter 2;125;6;2011 Quarter 3;105;7;2011 Quarter 4;90;8;b) (5 points) Copy the data into Excel and run the corresponding multiple regression. Write the estimated multiple regression equation use the variables defined above. (Hint: No need to conduct backwards elimination at this point.);c) (5 points) Explain the meaning of the slopes for seasonally dummy variable,, and. (Note: Use actual variable name and numbers to answer the questions. Put numbers in the right context.);d) (5 points) Test the overall fitness of the model. (State the hypotheses, and use Significant F to complete your test.);e) (Bonus 5 points) Which variables in the current regression model are significant? And which are not significant? Justify your answer.
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