- 7.2.1E: The length of life of brand X light bulbs is assumed to be N(?X, 78...
- 7.2.2E: Let X1,X2, . . . ,X5 be a random sample of SAT mathematics scores, ...
- 7.2.3E: Independent random samples of the heights of adult males living in ...
- 7.2.4E: [Medicine and Science in Sports and Exercise (January 1990).] Let X...
- 7.2.5E: A biologist who studies spiders was interested in comparing the len...
- 7.2.6E: A test was conducted to determine whether a wedge on the end of a p...
- 7.2.7E: An automotive supplier is considering changing its electrical wire ...
- 7.2.8E: Let and S2Y be the respective sample means and unbiased estimates o...
- 7.2.9E: Students in a semester-long health-fitness program have their perce...
- 7.2.10E: Twenty-four 9th- and 10th-grade high school girls were put on an ul...
- 7.2.11E: The Biomechanics Lab at Hope College tested healthy old women and h...
- 7.2.12E: Let X and Y equal the hardness of the hot and cold water, respectiv...
- 7.2.13E: Ledolter and Hogg (see References) report that two rubber compounds...
- 220.127.116.11-1: The length of life of brand X light bulbs is assumed to be N(X , 78...
- 18.104.22.168-2: Let X1, X2, ... , X5 be a random sample of SAT mathematics scores, ...
- 22.214.171.124-3: Independent random samples of the heights of adult males living in ...
- 126.96.36.199-4: [Medicine and Science in Sports and Exercise (January 1990).] Let X...
- 188.8.131.52-5: A biologist who studies spiders was interested in comparing the len...
- 184.108.40.206-6: A test was conducted to determine whether a wedge on the end of a p...
- 220.127.116.11-7: An automotive supplier is considering changing its electrical wire ...
- 18.104.22.168-8: Let X, Y, S2 X , and S2 Y be the respective sample means and unbias...
- 22.214.171.124-9: Students in a semester-long health-fitness program have their perce...
- 126.96.36.199-10: Twenty-four 9th- and 10th-grade high school girls were put on an ul...
- 188.8.131.52-11: The Biomechanics Lab at Hope College tested healthy old women and h...
- 184.108.40.206-12: Let X and Y equal the hardness of the hot and cold water, respectiv...
- 220.127.116.11-13: Ledolter and Hogg (see References) report that two rubber compounds...
- 18.104.22.168-14: Let S2 X and S2 Y be the respective variances of two independent ra...
Solutions for Chapter 7.2: Interval Estimation
Full solutions for Probability and Statistical Inference | 9th Edition
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
All possible (subsets) regressions
A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions
See Arithmetic mean.
An equation for a conditional probability such as PA B ( | ) in terms of the reverse conditional probability PB A ( | ).
Bivariate normal distribution
The joint distribution of two normal random variables
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
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.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
The probability of an event given that the random experiment produces an outcome in another event.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
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 .
Formulas used to determine the number of elements in sample spaces and events.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
A study in which a sample from a population is used to make inference to the population. See Analytic study
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.
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.
Finite population correction factor
A term in the formula for the variance of a hypergeometric random variable.
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
Effects in a fractional factorial experiment that are used to construct the experimental tests used in the experiment. The generators also deine the aliases.