- 6.11.1: A random sample of size 11 from a normal distribution has variance ...
- 6.11.2: A random sample of size 29 from a normal distribution has variance ...
- 6.11.3: Scores on an IQ test are normally distributed. A sample of 25 IQ sc...
- 6.11.4: A machine that fills beverage cans is supposed to put 12 ounces of ...
- 6.11.5: A sample of 25 one-year-old girls had a mean weight of 24.1 pounds ...
- 6.11.6: The 2008 General Social Survey asked a large number of people how m...
- 6.11.7: Scores on the math SAT are normally distributed. A sample of 20 SAT...
- 6.11.8: One of the ways in which doctors try to determine how long a single...
- 6.11.9: Find the upper 5% point of F7,20.
- 6.11.10: Find the upper 1% point of F2,5.
- 6.11.11: An F test with five degrees of freedom in the numerator and seven d...
- 6.11.12: A broth used to manufacture a pharmaceutical product has its sugar ...
- 6.11.13: Refer to Exercise 11 in Section 5.6. Can you conclude that the vari...
- 6.11.14: Refer to Exercise 13 in Section 5.6. Can you conclude that the time...
Solutions for Chapter 6.11: Tests for Variances of Normal Populations
Full solutions for Statistics for Engineers and Scientists | 4th Edition
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
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.
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
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
Coeficient of determination
See R 2 .
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.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.
Defects-per-unit control chart
See U chart
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
The response variable in regression or a designed experiment.
A matrix that provides the tests that are to be conducted in an experiment.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
A model to relate a response to one or more regressors or factors that is developed from data obtained from the system.
Error mean square
The error sum of squares divided by its number of degrees of freedom.
The variance of an error term or component in a model.
The distribution of the random variable deined as the ratio of two independent chi-square random variables, each divided by its number of degrees of freedom.
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.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials