 5.1: Your Statistics teacher has announced that the lower of your two te...
 5.2: In 1995 the Educational Testing Service (ETS) adjusted the scores o...
 5.3: A company manufactures wheels for inline skates. The diameters of ...
 5.4: As a group, the Dutch are among the tallest people in the world. Th...
 5.5: Suppose it takes you 20 minutes, on average, to drive to school, wi...
 5.6: Cold U? A high school senior uses the Internet to get information o...
 5.7: Stats test, Part II Suppose your Statistics professor reports test ...
 5.8: Checkup One of the authors has an adopted grandson whose birth fami...
 5.9: Stats test, part III The mean score on the Stats exam was 75 points...
 5.10: Mensa People with zscores above 2.5 on an IQ test are sometimes cl...
 5.11: Temperatures A towns January high temperatures average 36F with a s...
 5.12: Placement exams An incoming freshman took her colleges placement ex...
 5.13: Combining test scores The first Stats exam had a mean of 65 and a s...
 5.14: Combining scores again The first Stat exam had a mean of 80 and a s...
 5.15: Final exams Anna, a language major, took final exams in both French...
 5.16: MP3s Two companies market new batteries targeted at owners of perso...
 5.17: Cattle The Virginia Cooperative Extension reports that the mean wei...
 5.18: Car speeds John Beale of Stanford, CA, recorded the speeds of cars ...
 5.19: More cattle Recall that the beef cattle described in Exercise 17 ha...
 5.20: Car speeds again For the car speed data of Exercise 18, recall that...
 5.21: Cattle, part III Suppose the auctioneer in Exercise 19 sold a herd ...
 5.22: Caught speeding Suppose police set up radar surveillance on the Sta...
 5.23: Professors A friend tells you about a recent study dealing with the...
 5.24: Rock concerts A popular band on tour played a series of concerts in...
 5.25: Guzzlers? Environmental Protection Agency (EPA) fuel economy estima...
 5.26: IQ Some IQ tests are standardized to a Normal model, with a mean of...
 5.27: Small steer In Exercise 17 we suggested the model N(1152, 84) for w...
 5.28: High IQ Exercise 26 proposes modeling IQ scores with N(100, 16). Wh...
 5.29: College hoops The winning scores of all college mens basketball gam...
 5.30: Rivets A company that manufactures rivets believes the shear streng...
 5.31: Trees A forester measured the diameters of 27 trees in a woods, and...
 5.32: Car speeds, the picture For the car speed data of Exercise 18, here...
 5.33: Wisconsin ACT math The histogram shows the distribution of mean ACT...
 5.34: Wisconsin ACT math II This plot shows the mean ACT scores for Wisco...
 5.35: Winter Olympics 2010 downhill Fiftynine men qualified for the mens...
 5.36: Check the model The mean of the 100 car speeds in Exercise 20 was 2...
 5.37: Receivers 2010 This histogram displays NFL data from the 2010 footb...
 5.38: Customer database A large philanthropic organization keeps records ...
 5.39: Normal cattle Using N(1152, 84), the Normal model for weights of An...
 5.40: IQs revisited Based on the Normal model N(100, 16) describing IQ sc...
 5.41: More cattle Based on the model N(1152, 84) describing Angus steer w...
 5.42: More IQs In the Normal model N(100, 16), what cutoff value bounds a...
 5.43: Cattle, finis Consider the Angus weights model N(1152, 84) one last...
 5.44: IQ, finis Consider the IQ model N(100, 16) one last time. a) What I...
 5.45: Cholesterol Assume the cholesterol levels of adult American women c...
 5.46: Tires A tire manufacturer believes that the treadlife of its snow t...
 5.47: Kindergarten Companies that design furniture for elementary school ...
 5.48: Body temperatures Most people think that the normal adult body temp...
 5.49: Eggs Hens usually begin laying eggs when they are about 6 months ol...
 5.50: Tomatoes Agricultural scientists are working on developing an impro...
Solutions for Chapter 5: The Standard Deviation as a Ruler and the Normal Model
Full solutions for Stats Modeling the World  4th Edition
ISBN: 9780321854018
Solutions for Chapter 5: The Standard Deviation as a Ruler and the Normal Model
Get Full SolutionsStats Modeling the World was written by and is associated to the ISBN: 9780321854018. Chapter 5: The Standard Deviation as a Ruler and the Normal Model includes 50 full stepbystep solutions. This textbook survival guide was created for the textbook: Stats Modeling the World, edition: 4. Since 50 problems in chapter 5: The Standard Deviation as a Ruler and the Normal Model have been answered, more than 59916 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

aerror (or arisk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

Acceptance region
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

Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

Average
See Arithmetic mean.

Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

Block
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.

Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

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.

Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.

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

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff between false alarms and the detection of assignable causes.

Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.

Dependent variable
The response variable in regression or a designed experiment.

Dispersion
The amount of variability exhibited by data

Empirical model
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.

Error of estimation
The difference between an estimated value and the true value.

Exhaustive
A property of a collection of events that indicates that their union equals the sample space.

Harmonic mean
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .

Hat matrix.
In multiple regression, the matrix H XXX X = ( ) ? ? 1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .