- 7.1.1: Compute the correlation coefficient for the following data set. x 1...
- 7.1.2: For each of the following data sets, explain why the correlation co...
- 7.1.3: For each of the following scatterplots, state whether the correlati...
- 7.1.4: True or false, and explain briefly: a. If the correlation coefficie...
- 7.1.5: An investigator collected data on heights and weights of college st...
- 7.1.6: In a study of ground motion caused by earthquakes, the peak velocit...
- 7.1.7: A chemical engineer is studying the effect of temperature and stirr...
- 7.1.8: Another chemical engineer is studying the same process as in Exerci...
- 7.1.9: Tire pressure (in kPa) was measured for the right and left front ti...
- 7.1.10: In a sample of 300 steel rods, the correlation coeffi- cient betwee...
- 7.1.11: The article Drift in Posturography Systems Equipped with a Piezoele...
- 7.1.12: Phonics is an instructional method in which children are taught to ...
- 7.1.13: The article Little Ice Age Proxy Glacier Mall Balance Records Recon...
- 7.1.14: A scatterplot contains four points: (2,2), (1,1), (0,0), and (1,1)....
Solutions for Chapter 7.1: Correlation
Full solutions for Statistics for Engineers and Scientists | 4th Edition
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
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.
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.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
The variance of the conditional probability distribution of a random variable.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
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 .
A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X Y, ) [( )( )] =? ? E X Y ? ? X Y .
Another name for factors that are arranged in a factorial experiment.
A subset of effects in a fractional factorial design that deine the aliases in the design.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
A probability distribution for a discrete random variable
The amount of variability exhibited by data
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 of estimation
The difference between an estimated value and the true value.
A subset of a sample space.
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.
Fraction defective control chart
See P chart