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#1. (Related to Hypothesis Testing) When the population standard deviation ? is known, we compute a Z test statistic for the population average as


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#1. (Related to Hypothesis Testing) When the population standard deviation ? is known, we compute a Z test statistic for the population average as follows: n X Z σ μ = where is the sample mean, ? is the population mean, and n is the sample size. a) Using your own words, explain the meaning of the non-rejection region in hypothesis testing. b) What does it mean when the test statistic Z equals 0 for a 95% confidence level with Z critical values of ± 1.96? c) How do you modify the test statistic equation above when the population standard deviation is not known? #2. ( Related Hypothesis Testing ) After a year working as the new manager at a small financial consulting firm, the new manager wishes to analyze the performance of his staff compared to last year. He focuses on analyzing “time spent per customer on the phone”. The amount of time a financial consultant spent prior to the new manager’s arrival at that firm had a population mean of ? = 70 minutes. He gathers data by observing 41 phone calls made by several financial consultants and records the amount of time spent on the phone (in minutes). He enters the data in Excel 2007 and gets the following descriptive statistics (from Excel menu he clicks on “Data” clicks on “Data Analysis” selects “Descriptive Statistics” from the list selects the 41 data points and marks “Summary Statistics” and “Confidence Level for Mean = 95%”). Descriptive Statistics of "Time Spent" Mean 64.32 Standard Error 2.62 Median 61.00 Mode 60.00 Standard Deviation 16.81 Sample Variance 282.47 Kurtosis 0.25 Skewness 0.54 1 X
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Range 71.00 Minimum 37.00 Maximum 108.00 Sum 2637.00 Count 41 Confidence Level(95.0%) 5.30 From the output above the new manager notices that the average time spent under him is now lower, = 64.32 minutes, and that a 95% confidence level gives a margin of error of ± 5.30 minutes. But he does not know what to do with these results from the Excel output. Help the new manager assess his staff performance under two scenarios: Scenario 1: New manager is focused on cutting costs. Scenario 2: New manager is focused on improving customer satisfaction. a) Under each of the scenarios above, what can you tell him in terms of his staff performance? Why? b) What would happen to the confidence interval above if you take a larger sample size of n = 200 calls? Why? c) EXTRA CREDIT OF UP TO 5 POINTS: Would you conclude that a sample size of n = 41 calls is statistically and economically significant considering that over the course of a year the consultants at this company usually make a total of 10,000 calls? Why? #3. (Related to Regression Analysis ) Give an example of a regression model in a business setting. Explain in detail. 2 X
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