- 8.2.15: Let m denote the true average reaction time to a certainstimulus. F...
- 8.2.16: Newly purchased tires of a particular type are supposedto be filled...
- 8.2.17: Answer the following questions for the tire problem inExample 8.7.a...
- 8.2.18: Reconsider the paint-drying situation of Example 8.5, inwhich dryin...
- 8.2.19: The melting point of each of 16 samples of a certainbrand of hydrog...
- 8.2.20: Lightbulbs of a certain type are advertised as having anaverage lif...
- 8.2.21: The desired percentage of SiO2 in a certain type of aluminouscement...
- 8.2.22: To obtain information on the corrosion-resistance propertiesof a ce...
- 8.2.23: Automatic identification of the boundaries of significantstructures...
- 8.2.24: Unlike most packaged food products, alcohol beveragecontainer label...
- 8.2.25: Body armor provides critical protection for lawenforcement personne...
- 8.2.26: The recommended daily dietary allowance for zincamong males older t...
- 8.2.27: Show that for any D . 0, when the population distributionis normal ...
- 8.2.28: For a fixed alternative value m9, show that b(m9) S 0as n S ` for e...
Solutions for Chapter 8.2: z Tests for Hypotheses about a Population Mean
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th 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
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
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
The probability of an event given that the random experiment produces an outcome in another event.
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
A subset of effects in a fractional factorial design that deine the aliases in the design.
A probability distribution for a discrete random variable
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
The variance of an error term or component in a model.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
Fisher’s least signiicant difference (LSD) method
A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications
A function that is used to determine properties of the probability distribution of a random variable. See Moment-generating function