 9.6.1E: ?For the data given in Exercise 6.53, use a \(t\) test to test \(H...
 9.6.2E: ?For the data given in Exercise 6.54, use a \(t\) test to test \(H...
 9.6.3E: (In some of the exercises that follow, we must make assumptions of ...
 9.6.4E: ?In bowling, it is often possible to score well in the first game a...
 9.6.5E: (In some of the exercises that follow, we must make assumptions of ...
 9.6.6E: ?By squaring the binomial expression \(\left[\left(Y_{i}\bar{Y}\ri...
 9.6.7E: (In some of the exercises that follow, we must make assumptions of ...
 9.6.8E: (In some of the exercises that follow, we must make assumptions of ...
 9.6.9E: ?Show that when \(\rho=0\),(a) The points of inflection for the gra...
 9.6.10E: ?In a college health fitness program, let \(X\) equal the weight in...
 9.6.11E: (In some of the exercises that follow, we must make assumptions of ...
 9.6.12E: ?In Exercise 6.55, data are given for horsepower, the time it take...
 9.6.9.61: For the data given in Exercise 6.53, use a t test to test H0: = 0 ...
 9.6.9.62: For the data given in Exercise 6.54, use a t test to test H0: = 0 ...
 9.6.9.63: A random sample of size n = 27 from a bivariate normal distribution...
 9.6.9.64: In bowling, it is often possible to score well in the first game an...
 9.6.9.65: A random sample of size 28 from a bivariate normal distribution yie...
 9.6.9.66: By squaring the binomial expression [(Yi Y) (SxY /s2 x)(xi x)], sho...
 9.6.9.67: To help determine whether gallinules selected their mate on the bas...
 9.6.9.68: In sampling from a bivariate normal distribution, it is true that t...
 9.6.9.69: Show that when = 0, (a) The points of inflection for the graph of t...
 9.6.9.610: In a college health fitness program, let X equal the weight in kilo...
 9.6.9.611: Let X and Y have a bivariate normal distribution with correlation c...
 9.6.9.612: In Exercise 6.55, data are given for horsepower, the time it takes...
Solutions for Chapter 9.6: More Tests
Full solutions for Probability and Statistical Inference  9th Edition
ISBN: 9780321923271
Solutions for Chapter 9.6: More Tests
Get Full SolutionsSince 24 problems in chapter 9.6: More Tests have been answered, more than 296406 students have viewed full stepbystep solutions from this chapter. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. Chapter 9.6: More Tests includes 24 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9.

Arithmetic mean
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

Attribute
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

Bimodal distribution.
A distribution with two modes

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).

Coeficient of determination
See R 2 .

Comparative experiment
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.

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.

Confounding
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.

Conidence coeficient
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.

Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.

Correction factor
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 .

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Distribution function
Another name for a cumulative distribution function.

Error propagation
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.

Expected value
The expected value of a random variable X is its longterm 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.

Experiment
A series of tests in which changes are made to the system under study

Fisher’s least signiicant difference (LSD) method
A series of pairwise hypothesis tests of treatment means in an experiment to determine which means differ.

Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

Fraction defective
In statistical quality control, that portion of a number of units or the output of a process that is defective.

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.