- 7.3.49: Songs on an iPod Davids iPod has about 10,000 songs. The distributi...
- 7.3.50: Making auto parts A grinding machine in an auto parts plant prepare...
- 7.3.51: Songs on an iPod Refer to Exercise 49. How many songs would you nee...
- 7.3.52: Making auto parts Refer to Exercise 50. How many axles would you ne...
- 7.3.53: Larger sample Suppose that the blood cholesterol level of all men a...
- 7.3.54: Dead battery? A car company has found that the lifetime of its batt...
- 7.3.55: ?Bottling cola A bottling company uses a filling machine to fill pl...
- 7.3.56: Cereal A companys cereal boxes advertise 9.65 ounces of cereal. In ...
- 7.3.57: What does the CLT say? Asked what the central limit theorem says, a...
- 7.3.58: What does the CLT say? Asked what the central limit theorem says, a...
- 7.3.59: Songs on an iPod Refer to Exercise 49. (a) Explain why you cannot s...
- 7.3.60: Lightning strikes The number of lightning strikes on a square kilom...
- 7.3.61: Airline passengers get heavier In response to the increasing weight...
- 7.3.62: How many people in a car? A study of rush-hour traffic in San Franc...
- 7.3.63: More on insurance An insurance company claims that in the entire po...
- 7.3.64: Bad carpet The number of flaws per square yard in a type of carpet ...
- 7.3.65: ?Multiple choice:Scores on the mathematics part of the SAT exam in ...
- 7.3.66: ?Multiple choice: Why is it important to check the 10% condition be...
- 7.3.67: Multiple choice: Select the best answer for Exercises 65 to 68. A n...
- 7.3.68: Multiple choice: Select the best answer for Exercises 65 to 68. The...
- 7.3.69: Exercises 69 to 72 refer to the following setting. In the language ...
- 7.3.70: Exercises 69 to 72 refer to the following setting. In the language ...
- 7.3.71: Exercises 69 to 72 refer to the following setting. In the language ...
- 7.3.72: Exercises 69 to 72 refer to the following setting. In the language ...
Solutions for Chapter 7.3: Sample Means
Full solutions for The Practice of Statistics | 5th Edition
Summary of Chapter 7.3: Sample Means
Sample proportions arise most often when we are interested in categorical variables. You learned about the shape, center, and spread of the sampling distribution of a sample mean. When the population is Normal. Also to explain how the shape of the sampling distribution is affected by the shape of the population distribution and the sample size.
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
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.
See Arithmetic mean.
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.
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.
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.
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
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.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).
The response variable in regression or a designed experiment.
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model-itting process and not on replication.
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.
A series of tests in which changes are made to the system under study
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
In statistical quality control, that portion of a number of units or the output of a process that is defective.
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 .