STATISTICAL ANALYSIS (No long explanation needed. Rate will be given and write the complete solutions.) CI on Mean, Variance Unknown, Prediction and Tolerance Interval A CNC (computer numerical control) machine produces iron automobile crankshafts. Samples are measured and the inner diameter are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 centimeters. For all computations, assume an approximately normal distribution. The sample mean and standard deviation for the given data are = 1.0056, and s = 0.0246. Find a 99% confidence interval on the mean of diameter. Compute a 99% prediction interval on a measured diameter of a single crankshaft piece taken from the machine. Find the 99% tolerance limits that will contain most of the metal pieces produced by the CNC machine. Choose the correct answer. a. CI on the mean: 0.970 < μ < 1.9845. Prediction Interval: 0.9186 ≤ Xn+1 ≤ 1.0926. Tolerance Interval (0.8937 and 1.1175) b. CI on the mean: 0.9781 < μ < 1.0331. Prediction Interval: 0.9186 ≤ Xn+1 ≤ 1.0926. Tolerance Interval (0.8937 and 1.1175). Insufficient data to compute for the Tolerance Interval c. Insufficient data to compute. Missing the sample size n d. CI on the mean: 0.9781 < μ < 1.0331. Prediction Interval: 0.9186 ≤ Xn+1 ≤ 1.0926. Tolerance Interval (0.8937 and 1.1175)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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STATISTICAL ANALYSIS (No long explanation needed. Rate will be given and write the complete solutions.)

CI on Mean, Variance Unknown, Prediction and Tolerance Interval

A CNC (computer numerical control) machine produces iron automobile crankshafts. Samples are measured and the inner diameter are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 centimeters. For all computations, assume an approximately normal distribution. The sample mean and standard deviation for the given data are = 1.0056, and s = 0.0246.

Find a 99% confidence interval on the mean of diameter. Compute a 99% prediction interval on a measured diameter of a single crankshaft piece taken from the machine. Find the 99% tolerance limits that will contain most of the metal pieces produced by the CNC machine.

Choose the correct answer.

a. CI on the mean: 0.970 < μ < 1.9845. Prediction Interval: 0.9186 ≤ X_n+1 ≤ 1.0926. Tolerance Interval (0.8937 and 1.1175)

b. CI on the mean: 0.9781 < μ < 1.0331. Prediction Interval: 0.9186 ≤ X_n+1 ≤ 1.0926. Tolerance Interval (0.8937 and 1.1175). Insufficient data to compute for the Tolerance Interval

c. Insufficient data to compute. Missing the sample size n

d. CI on the mean: 0.9781 < μ < 1.0331. Prediction Interval: 0.9186 ≤ X_n+1 ≤ 1.0926. Tolerance Interval (0.8937 and 1.1175)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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