14. Simulated Data: Minitab is designed to generate random numbers from a variety of different sampling distributions. In this experiment we will generate 800 IQ scores, then we will construct a...

Extracted text: 14. Simulated Data: Minitab is designed to generate random numbers from a variety of different sampling distributions. In this experiment we will generate 800 IQ scores, then we will construct a confidence interval based on the sample results. IQ scores have a normal distribution with a mean of 100 and a standard deviation of 15. First generate the 800 sample values as follows. 1. Click on Calc, then select Random Data, then Normal. 2. In the dialog box, enter a sample size of 800, a mean of 100, and a standard deviation of 15. Specify column C1 as the location for storing the results. Click OK. 3. Use Stat/Basic Statistics/Display Descriptive Statistics to find these statistics: n = S = Using the generated values, construct a 95% confidence interval estimate of the population mean of all IQ scores. Enter the 95% confidence interval here. Because of the way that the sample data were generated, we know that the population mean is 100. Do the confidence interval limits contain the true mean IQ score of 100? If this experiment were to be repeated over and over again, how often would we expect the confidence interval limits to contain the true population mean value of 100? Explain how you arrived at your answer. 15. Quality Control of Doughnuts: The Hudson Valley Bakery makes doughnuts that are packaged in boxes with labels stating that there are 12 doughnuts weighing a total of 42 oz. If the variation among the doughnuts is too large, some boxes will be underweight (cheating consumers) and others will be overweight (lowering profit). A consumer would not be happy with a doughnut so small that it can be seen only with an electron microscope, nor would a consumer be happy with a doughnut so large that it resembles a tractor tire. The quality-control supervisor has found that he can stay out of trouble if the doughnuts have a mean of 3.50 oz. and a standard deviation of 0.06 oz. or less. Twelve doughnuts are randomly selected from the production line and weighed, with the result given here (in ounces). 3.43 3.37 3.58 3.50 3.68 3.61 3.42 3.52 3.66 3.50 3.36 3.42 Construct a 95% confidence interval for o, and then determine whether the quality- control supervisor is in trouble.


Extracted text: 13. Confidence Interval for Estimating a Mean: Lists sample weights of the cola in cans of regular Coke. Those weights are listed below: Weights (in pounds) of a sample of cans of regular Coke: 0.8150 0.8192 0.8163 0.8211 0.8181 0.8247 0.8062 0.8128 0.8172 0.8110 0.8251 0.8264 0.7901 0.8244 0.8073 0.8079 0.8044 0.8170 0.8161 0.8194 0.8189 0.8194 0.8176 0.8284 0.8165 0.8143 0.8229 0.8150 0.8152 0.8244 0.8207 0.8152 0.8126 0.8295 0.8161 0.8192 a. Use Minitab to find the following confidence interval estimates of the population mean. 99.5 % confidence interval: 99% confidence interval: 98% confidence interval: 95% confidence interval: 90% confidence interval: b. Change the first weight from 0.8192 lb. to 8192 lb. (a common error in data entry) and find the indicated confidence intervals for the population mean. 99.5% confidence interval: 99% confidence interval: 98% confidence interval: 95% confidence interval: 90% confidence interval: c. By comparing these results from parts (a) and (b), what do you conclude about the effect of an outlier on the values of the confidence interval limits?