- 13-7.1: Testing for Bias The last 106 baseball seasons (as of this writing)...
- 13-7.2: Notation Listed below are the most recent (as of this writing) winn...
- 13-7.3: Runs Test If we use a 0.05 significance level to test for randomnes...
- 13-7.4: Good Sample? Given a sequence of data, such as the one from Exercis...
- 13-7.5: Using the Runs Test for Randomness. In Exercises 510, use the runs ...
- 13-7.6: Using the Runs Test for Randomness. In Exercises 510, use the runs ...
- 13-7.7: Using the Runs Test for Randomness. In Exercises 510, use the runs ...
- 13-7.8: Using the Runs Test for Randomness. In Exercises 510, use the runs ...
- 13-7.9: Runs Test with Large Samples. In Exercises 912, use the runs test w...
- 13-7.10: Runs Test with Large Samples. In Exercises 912, use the runs test w...
- 13-7.11: Runs Test with Large Samples. In Exercises 912, use the runs test w...
- 13-7.12: Runs Test with Large Samples. In Exercises 912, use the runs test w...
- 13-7.13: Finding Critical Values a. Using all of the elements A, A, A, B, B,...
Solutions for Chapter 13-7: Runs Test for Randomness
Full solutions for Elementary Statistics | 12th Edition
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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
Bivariate normal distribution
The joint distribution of two normal random variables
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.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
Chi-square (or chi-squared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.
Conditional probability distribution
The distribution of a random variable given that the random experiment produces an outcome in an event. The given event might specify values for one or more other random variables
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
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 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.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
Discrete random variable
A random variable with a inite (or countably ininite) range.
A subset of a sample space.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .