- 6.1.1: In an experiment to measure the lifetimes of parts manufactured fro...
- 6.1.2: A simple random sample consists of 65 lengths of piano wire that we...
- 6.1.3: The article Supply Voltage Quality in Low-Voltage Industrial Networ...
- 6.1.4: The pH of an acid solution used to etch aluminum varies somewhat fr...
- 6.1.5: Recently many companies have been experimenting with telecommuting,...
- 6.1.6: A certain type of stainless steel powder is supposed to have a mean...
- 6.1.7: When it is operating properly, a chemical plant has a mean daily pr...
- 6.1.8: Lasers can provide highly accurate measurements of small movements....
- 6.1.9: The article Predicting Profit Performance for Selecting Candidate I...
- 6.1.10: A new concrete mix is being designed to provide adequate compressiv...
- 6.1.11: Fill in the blank: If the null hypothesis is H0 : 5, then the mean ...
- 6.1.12: Fill in the blank: In a test of H0 : 10 versus H1 : < 10, the sampl...
- 6.1.13: The following MINITAB output presents the results of a hypothesis t...
- 6.1.14: The following MINITAB output presents the results of a hypothesis t...
Solutions for Chapter 6.1: Large-Sample Tests for a Population Mean
Full solutions for Statistics for Engineers and Scientists | 4th Edition
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
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
See Arithmetic mean.
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defects-per-unit or U chart.
Coeficient of determination
See R 2 .
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous 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.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
Another term for the conidence coeficient.
A probability distribution for a continuous random variable.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
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 .
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 sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
A subset of effects in a fractional factorial design that deine the aliases in the design.
The response variable in regression or a designed experiment.
A property of a collection of events that indicates that their union equals the sample space.
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.