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QUESTION 1: A manufacturer of sprinkler systems used for fire protection has a specification that the system activation temperature be 130 F. A sample of 9 systems yields a sample average of 131.08 F. If the distribution of activation temperatures is normal with standard deviation known to be 1.5 F, does the data contradict the manufactures claim at the 1% level of significance? 1. 2. 3. 4. 5. 6. 7. 8. QUESTION 2: A journal article presented measurements over 22 data points and the findings were: The sample mean is x = 13.71, and the sample standard deviation is S = 3.55. Find a 95% confidence interval on the population mean. QUESTION 3: Similar to Question 2 above, another journal article collected measurements over a larger sample of 92 data points and the findings were as above: The sample mean is x = 13.71, and the sample standard deviation is S = 3.55. Find a 99% confidence interval on the population mean. QUESTION 4: A random sample of 15 pistons (from internal combustion engines) is selected from a large population whose diameters are known to be normally distributed. If a piston is too large or too small it will not be useable, as it will not fit inside a cylinder, or have too much clearance. The sample standard deviation of piston diameters is 2.0 mm. Find a 95% confidence interval for the population variance. QUESTION 5. A camera is housed on the end of a vibrating rod. To take a high quality image, the variance in the position of the camera must stay within a value of 0.1 (in)2. Snapshots are taken 32 times resulting in a sample variance of camera position being 0.115 (in)2. Is there evidence to suggest that the camera will have a problem with the quality of its image? Test the hypothesis at 5% significance level. 1. 2. 3. 4. 5. 6. 7. QUESTION 6. Spacer collars are manufactured by a machine which should produce a mean thickness of 39 mm: too thick or thin means that the collars are not useable. A sample of six collars is collected and the data is (in millimeters): 39.030, 38.997, 39.012, 39.008, 39.019, 39.002 Test the hypothesis that the machine is producing collars to specification at the 1% level. 1. 2. 3. 4. 5. 6. 7. QUESTION 7. Reconsider the spacer collars in Question 6 where it is now revealed to you that the population is known to be normally distributed with a population standard deviation of 0.01 mm. A sample of six collars is collected and the data is (the same as QUESTION 6): 39.030, 38.997, 39.012, 39.008, 39.019, 39.002 Test the hypothesis that the machine is producing collars to specification at the 1% level. 1. 2. 3. 4. 5. 6. 7.

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Advanced Statistics Questions
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