Answered: The refereed question A random sample…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The refereed question A random sample of 12 shearing pins is taken in a study of the Rockwell hardness of the pin head. Measurements on the Rockwell hardness are made for each of the 12, yielding an average value of 48.50 with a sample standard deviation of 1.5. Assuming the mea- surements to be normally distributed, construct a 90% confidence interval for the mean Rockwell hardness.

Transcribed Image Text:8:10 Done 50 college stu- s and a stan- for the mean mce about the ate the mean 74.5 centime- owners in the le is driven on standard de- listribution of al. for the aver- bile is driven mce about the ate the aver- car owners in year? rcise 9.2 if we mean will be =rcise 9.3 if we mean will be rmine the av- es in a certain e need to be be within 15 t it is known s. ed cereals con- other degen- Hucted by Dr. of Health and d Dietetics at sample con- pha-Bits, the th a standard he sugar con- t a 95% con- ent for single Walpole ber of words typed per minute, find a 95% confidence interval for the average number of words typed by all graduates of this school. 9.11 A machine produces metal pieces that are cylin- drical in shape. A sample of pieces is taken, and the diameters are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 centimeters. Find a 99% con- fidence interval for the mean diameter of pieces from this machine, assuming an approximately normal dis- tribution. 9.12 A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories per bar, with a standard deviation of 15 calories. Construct a 99% confidence interval for the true mean calorie con- tent of this brand of energy bar. Assume that the dis- tribution of the calorie content is approximately nor- mal. 9.13 A random sample of 12 shearing pins is taken in a study of the Rockwell hardness of the pin head. Measurements on the Rockwell hardness are made for each of the 12, yielding an average value of 48.50 with a sample standard deviation of 1.5. Assuming the mea- surements to be normally distributed, construct a 90% confidence interval for the mean Rockwell hardness. 9.14 The following measurements were recorded for the drying time, in hours, of a certain brand of latex. paint: 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.6 3.7 2.8 4.4 4.0 5.2 3.0 4.8 Assuming that the measurements represent a random sample from a normal population, find a 95% predic- tion interval for the drying time for the next trial of the paint. 9.15 Referring to Exercise 9.5, construct a 99% pre- diction interval for the kilometers traveled annually by an automobile owner in Virginia. 9.16 Consider Exercise 9.10. Compute the 95% pre- diction interval for the next observed number of words per minute typed by a graduate of the secretarial school. 9.17 Consider Exercise 9.9. Compute a 95% predic- tion interval for the sugar content of the next single serving of Alpha-Bits. 9.18 Referring to Exercise 9.13, construct a 95% tol- erance interval containing 90% of the measurements.

9.18 Referring to Exercise 9.13, construct a 95% tol-
erance interval containing 90% of the measurements.

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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