- 6.4.1: Statistical Literacy Binomial probability distributions depend on t...
- 6.4.2: Statistical Literacy When we use a normal distribution to approxima...
- 6.4.3: Critical Thinking You need to compute the probability of 5 or fewer...
- 6.4.4: Critical Thinking Consider a binomial experiment with 20 trials and...
- 6.4.5: Health: Lead Contamination More than a decade ago, high levels of l...
- 6.4.6: Insurance: Claims Do you try to pad an insurance claim to cover you...
- 6.4.7: Longevity: 90th Birthday It is estimated that 3.5% of the general p...
- 6.4.8: Fishing: Billfish Ocean fishing for billfish is very popular in the...
- 6.4.9: Grocery Stores: New Products The Denver Post stated that 80% of all...
- 6.4.10: Crime: Murder What are the chances that a person who is murdered ac...
- 6.4.11: Supermarkets: Free Samples Do you take the free samples offered in ...
- 6.4.12: Ice Cream: Flavors Whats your favorite ice cream flavor? For people...
- 6.4.13: Airline Flights: No-Shows Based on long experience, an airline foun...
- 6.4.14: General: Approximations We have studied two approximations to the b...
Solutions for Chapter 6.4: NORMAL DISTRIBUTIONS
Full solutions for Understandable Statistics | 9th 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
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.
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.
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 probability distribution for a continuous random variable.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
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.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial experiment.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
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.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
A probability distribution for a discrete random variable
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.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
The variance of an error term or component in a model.
Estimate (or point estimate)
The numerical value of a point estimator.
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.
Fraction defective control chart
See P chart
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 .