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Stat 302 Statistical Methods 1 (2) Question 1: A computer software package was used to calculate some numerical summaries of a sample of data. The results are displayed here: Variable : X , N=? , Mean=? , SE mean= 2.05 , StDev=10.25 , Variance=? Sum= 3761 , Sum of squares=? (a)Fill in the missing quantities (b)What is the estimate of the mean of the population from which this sample was drawn? Answer 1: (a)N=25 Mean=150.47 (b)150.468 Variance=105.06 SS=2521.5 Question 2: A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with standard deviation 0.001 millimeters. A random sample of 15 rings has a mean diameter 74.036 millimeters. (a)Construct a 99% two sided confidence interval on the mean piston ring diameter. (b)Construct a 99% lower confidence bound on the mean piston ring diameter. Compare the lower bound of this confidence interval with the one in part (a). Answer 2: (a)[74.0353 , 74.0367] (b)[74.035 , infinity] Question 3: A postmix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was found to have a mean syrup content 1.10 fluid ounce and a standard deviation of s= 0.015 fluid ounce. Find a 95% CI on the mean volume of syrup dispensed. Answer 3: [1.094 , 1.106] Question 4: The percentage of titanium is an alloy used in aerospoace castings is measured in 51 randomly selected parts. The sample standard deviation is 0.37. Construct a 95% two sided confidence intervals for standard deviation. Answer 4: [0.31 , 0.46]