- 8-4.1: Give three examples of proportions. Answers will vary.
- 8-4.2: Why is a proportion considered a binomial variable?
- 8-4.3: When you are testing hypotheses by using proportions, what are the ...
- 8-4.4: What are the mean and the standard deviation of a proportion? m _ n...
- 8-4.5: Home Ownership A recent survey found that 68.6% of the population o...
- 8-4.6: Stocks and Mutual Fund Ownership It has been found that 50.3% of U....
- 8-4.7: Overweight Children Health issues due to being overweight affect al...
- 8-4.8: Female Physicians The percentage of physicians who are women is 27....
- 8-4.9: Traveling Overseas Of U.S. residents traveling overseas, 47% were w...
- 8-4.10: Undergraduate Enrollment It has been found that 85.6% of all enroll...
- 8-4.11: Moviegoers The largest group of moviegoers by age is the 40- to 59-...
- 8-4.12: Exercise to Reduce Stress Asurvey by Mens Health magazine stated th...
- 8-4.13: After-School Snacks In the Journal of the American Dietetic Associa...
- 8-4.14: Natural Gas Heat The Energy Information Administration reported tha...
- 8-4.15: Youth Smoking Researchers suspect that 18% of all high school stude...
- 8-4.16: Television Set Ownership According to Nielsen Media Research, of al...
- 8-4.17: Borrowing Library Books For Americans using library services, the A...
- 8-4.18: Doctoral Students Salaries Nationally, at least 60% of Ph.D. studen...
- 8-4.19: Football Injuries Areport by the NCAAstates that 57.6% of football ...
- 8-4.20: Foreign Languages Spoken in Homes Approximately 19.4% of the U.S. p...
- 8-4.21: Coin Tossing A coin is tossed 9 times and 3 heads appear. Can you c...
- 8-4.22: First-Class Airline Passengers In the past, 20% of all airline pass...
- 8-4.23: Show that z _ can be derived from by substituting m _ np and s _ an...
Solutions for Chapter 8-4: z Test for a Proportion
Full solutions for Elementary Statistics: A Step by Step Approach 8th ed. | 8th Edition
2 k p - factorial experiment
A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average
Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.
Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability
Binomial random variable
A discrete random variable that equals the number of successes in a ixed number of Bernoulli trials.
The joint probability distribution of two random variables.
Bivariate normal distribution
The joint distribution of two normal random variables
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
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.
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks.
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).
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 .
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
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.
A subset of a sample space.
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
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