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ENGR 3302: Engineering Statistics and Experimentation Point and Interval Estimate of the Mean Objective: upon completion of this lab you should be able to a) determine the type of distribution for a given data. b) find the mean, the variance, and the standard deviation of known population, c) find the point estimate of the mean of unknown population, d) find the Confidence Interval (CI) of the mean for specified sample size and confidence level, e) determine the effect of the sample size and confidence level (CL) on the confidence interval. Task 1: A manufacture produces 10,000 resistors of size 1 KΩ every day. The values of the resistors are stored in the excel sheet “Data” in the course website. You can save the file to the desktop of the computer. You can open and copy the data directly from the excel sheet and paste them into the SPSS statistical software. You also can load the data into Matlab variable by executing the following commend >>ResistorVal = xlsread('C:\Documents and Settings\mbingabr\Desktop\Data.xls', 'Resistor'); You need to insert the actual location of the file in the first quote. The commend xlsread will open the excel file “Data” and read the data in the sheet labeled “Resistor”. It is not know the distribution of the resistors’ values. Do the following: a) Use the SPSS statistical software to determine if the resistors’ values follow a uniform or normal distribution. b) If the distribution is uniform then calculate the mean, the variance, and the standard deviation using the equations in Ch 4. Remember for uniform distribution you need to find the maximum and the minimum values to calculate the mean and the variance. c) Calculate the mean and the variance using all resistor values in the population. How do the mean and variance compare to the values found in part b. Task 2: Let us assume that you don’t have the time to measure 10,000 resistors to determine the distribution of the resistors’ values and then calculate the mean and the standard deviation. How will you estimate the mean? One way to do it is to take a simple random sample (SRS) and then estimate the parameter (mean) of the population from the statistic (mean) of the sample as we learned in chapter 5. You decided to take a sample of size 10 to estimate the mean. Find the following: a) The point estimate for the mean value of the resistors. How far is your point estimate of the mean (in percentage) from the actual value found in part c of task 1. b) The 95% CI for the mean value of the resistors by using the standard deviation of the sample s. c) The 95% CI for the mean value of the resistors by using the standard deviation of the population in task 1 part c. How different is the interval from the answer in part b and which one is more accurate? d) Does the actual mean in part c in task 1 fall within the confidence interval of the estimate found in part b? Task 3: Based on the results in task 2, you decided to increase the size of the sample to 50 to improve the estimate. Find the following when the size of the SRS is increased to n=50: a) The point estimate for the mean value of the resistors. How close is your estimate of the mean to the actual value found in part c of task 1. b) The 95% confidence interval for the mean value of the resistors using the standard deviation of the sample s. c) The 95% confidence interval for the mean value of the resistors using the standard deviation of the population in task 1 part c. How different is the interval from the answer in part b and which one is more accurate? d) Does the actual mean in part c of task 1 fall within the confidence interval of the estimate found in part b? e) You want to reduce the confidence interval found in part b by half without compromising the 95% confidence level. What should you do to accomplish this?