- 3.3.1: FindtheuncertaintyinY ,giventhat X = 2.0 0.3and a. Y = X3 b. Y = 2X...
- 3.3.2: Given that X and Y are related by the given equation, and that X = ...
- 3.3.3: The volume of a cone is given by V = r 2h/3, where r is the radius ...
- 3.3.4: The velocity V of sound in air at temperature T is given by V = 20....
- 3.3.5: The period T of a simple pendulum is given by T = 2 L/g where L is ...
- 3.3.6: The change in temperature of an iron bar brought about by a transfe...
- 3.3.7: The friction velocity F of water flowing through a pipe is given by...
- 3.3.8: The refractive index n of a piece of glass is related to the critic...
- 3.3.9: The density of a rock will be measured by placing it into a graduat...
- 3.3.10: The conversion of ammonium cyanide to urea is a second-order reacti...
- 3.3.11: Convert the following absolute uncertainties to relative uncertaint...
- 3.3.12: Convert the following relative uncertainties to absolute uncertaint...
- 3.3.13: The acceleration g due to gravity is estimated by dropping an objec...
- 3.3.14: Refer to Exercise 4. Assume that T = 298.4 0.2 K. Estimate V, and f...
- 3.3.15: Refer to Exercise 5. a. Assume g = 9.80 m/s2 exactly, and that L = ...
- 3.3.16: Refer to Exercise 6. Assume that c = 448 J/kg C and Q = 1210 J are ...
- 3.3.17: Refer to Exercise 7. Estimate F, and find the relative uncertainty ...
- 3.3.18: Refer to Exercise 8. Assume the critical angle is measured to be 0....
- 3.3.19: Refer to Exercise 9. Assume that the mass of the rock is 288.2 g wi...
- 3.3.20: In a chemical reaction run at a certain temperature, the concentrat...
Solutions for Chapter 3.3: Uncertainties for Functions of One Measurement
Full solutions for Statistics for Engineers and Scientists | 4th Edition
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
`-error (or `-risk)
In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error).
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
The joint probability distribution of two random variables.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
An estimator that converges in probability to the true value of the estimated parameter as the sample size increases.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
Estimate (or point estimate)
The numerical value of a point estimator.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.