s - Answer the following problems...BE SURE TO SHOW ALL WORK either on an excel spreadsheet or a word document. You are not to use SPSS. Use excel and place all answers and work on the template provided. 1. Consider the file data on Taxes that is included in worksheet P1 on the exam template. This data represents property taxes paid by 170 residents that live in a small town. Assume this file to be the entire population. Answer the following questions : (20 pts) a. Conduct a test at the alpha = .05 level to determine if there is a difference in taxes paid by another jurisdiction. The information on this other jurisdiction is population information. In this other jurisdiction, the mean taxes paid by 243 residents are $1802.68 with a population standard deviation of $141.62. b. What is the 95% confidence interval for the difference between the taxes paid in the two jurisdictions from problem a c. Conduct a test at the alpha = .05 level to determine if there is a difference between taxes paid in neighborhood 3 and in neighborhood 4. Use all the data points from both neighborhoods and consider this to be sample data. d. From part c, what is the 95% confidence interval for the difference between means in the two neighborhoods e. Conduct a test between neighborhoods 2 and 3, at alpha = .05 to see if the variances between the two neighborhoods are unequal 2. The following data represents the running time of films produced by 2 motion picture companies. Assume these are independent samples (15 pts) Company Company 1 Company 2 Time (in minutes) 102 86 98 81 165 97 109 134 92 92 87 114 Test the null hypothesis that the average running time of the films produced by company 2 exceeds the average running time of films produced by company 1 by an amount of 10 minutes. Test against the null hypothesis of a one sided alternative that the difference is more than 10 minutes. a) Perform the Hypothesis test at alpha = .1 b) Determine the confidence interval for the difference between the means at 90% CI 3. In an experiment designed to study the effects of illumination level on task performance, subjects were required to insert a fine-tipped probe into the eyeholes of ten needles in rapid succession both for light level with a black background and a higher level with a white background. Each data value is the time results (in seconds) to complete the task as shown here: Does the data indicate that the higher level of illumination yields a decrease of more than 5 seconds in the difference between task completion time? (Note, the data is also provided on worksheet P4. 10 pts) a. What is the most appropriate hypothesis test technique for this study? b. Conduct a test to see if there is if the higher level of illumination yields a decrease of more than 5 seconds at alpha = .05 level. Consider this statement to be the claim. Conduct the test while placing the claim on the Alternate Hypothesis. 4. Antipsychotic drugs are widely prescribed for conditions such as schizophrenia and bipolar disorder. A recent study reported on body composition and metabolic changes for individuals who have taken various antipsychotic drugs for short periods of time. Answer the following questions associated with this study (15 points) a. What are the upper and lower bound 95% confidence intervals for a sample of 41 patients who had taken aripipazole (an antipsychotic drug) and had a mean change in total cholesterol of 3.75 mg/dL and a standard error of 3.878? b. Another group of 36 patients have taken quetiapine as a drug to treat bipolar disorder. On average, the patients experienced a change in cholesterol level of 9.05 mg/dl with a standard error of 4.256. Conduct a test at the alpha = .05 level to determine if the true average cholesterol level changed due to the effects of taking quetiapine as a treatment for bipolar disorder. c. For a sample of 45 individuals who have taken olanzapine, the study reported a 95% confidence interval increase of cholesterol level to be 7.38 mg/dL and 9.69mg/dL. What are the 99% confidence interval values? 5. The manager of a computer repair service wants to determine whether there is a difference in the time it takes 4 technicians to repair 3 different brands of disk drives. The data in worksheet P5 shows the time (in minutes) it took each technician to repair the disk drives. Answer the following questions by using the best technique learned in class. Perform the test at the alpha of .10: (10 pts): a. b. c. d. Is there a different in the technicians' time to repair? Is there a difference in the disk drives Is there a difference in interaction effect between technicians and disk drives Briefly discuss the test result of (a,,b and c) with respect to any anomalies or unusual results that need further study for explanation. 6. Three different machines are being considered for use in manufacturing rubber seals. The machines are being compared with respect to tensile strength of the product. A random sample of 4 seals from each machine is used to determine whether the mean tensile strength varies from machine to machine. Perform an ANOVA test to determine whether the tensile strengths are equivalent for the three machines. Use alpha = .05. The following are tensile strength measurements in kilograms per square centimeter: (15 pts) 7. An engineering statistician wants to conduct a test to determine if there is a difference in the compression strength of two different manufactures of reinforced concrete columns. Each manufacturer has provided sample data for compression strength (column failure) as follows: (15 pts) Manufacturer 1: mean compression strength is 956 KSI based on 30 samples with a standard deviation of 192 KSI. Manufacturer 2: mean compression strength of 898 KSI based on 25 samples with a standard deviation of 256 KSI Conduct a test at alpha equal to .01 to see if there is a difference between the two different manufacturers. Consider the data to be from two different populations