- 5.1SE: A molecular biologist is studying the effectiveness of a particular...
- 5.2SE: Refer to Exercise 1. Another molecular biologist repeats the study ...
- 5.3SE: The article "Genetically Based Tolerance to Endosulfan, Chromium (V...
- 5.4SE: A sample of 87 glass sheets has a mean thickness of 4.20 mm with a ...
- 5.5SE: A sample of 125 pieces of yarn had mean breaking strength 6.1 N and...
- 5.6SE: Refer to Exercise 5. Additional pieces of yarn will be sampled in o...
- 5.7SE: Leakage from underground fuel tanks has been a source of water poll...
- 5.8SE: A new catalyst is being investigated for use in the production of a...
- 5.9SE: Three confidence intervals for the mean shear strength (in ksi) of ...
- 5.10SE: A pollster plans to survey a random sample of voters in a certain c...
- 5.11SE: In the article "Groundwater Electromagnetic Imaging in Complex Geol...
- 5.12SE: Polychlorinated biphenyls (PCBs) are a group of synthetic oil-like ...
- 5.13SE: A 99% confidence interval for a population mean based on a sample o...
- 5.14SE: A sample of 100 components is drawn, and a 95% confidence interval ...
- 5.15SE: A metallurgist makes several measurements of the melting temperatur...
- 5.16SE: In a study of the lifetimes of electronic components, a random samp...
- 5.17SE: The temperature of a certain solution is estimated by taking a larg...
- 5.18SE: Boxes of nails contain 100 nails each. A sample of 10 boxes is draw...
- 5.19SE: Let X represent the number of events that are observed to occur in ...
- 5.20SE: The answer to Exercise 19 part (d) is needed for this exercise. A g...
- 5.21SE: In a Couette flow, two large flat plates lie one atop another, sepa...
- 5.24SE: A sample of eight repair records for a certain fiber-optic componen...
- 5.25SE: Refer to Exercise 24.Asample of six repair records for a different ...
- 5.26SE: A sample of seven concrete blocks had their crushing strength measu...
- 5.27SE: Refer to Exercise 22.a. Generate 10,000 bootstrap samples from the ...
Solutions for Chapter 5: Statistics for Engineers and Scientists 4th Edition
Full solutions for Statistics for Engineers and Scientists | 4th Edition
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test
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
See Arithmetic mean.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
A subset of a sample space.
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.