proportional

Examples of proportional in the following topics:

• Proportion

• Comparing Two Independent Population Proportions

  • Comparing two proportions, like comparing two means, is common.
  • A hypothesis test can help determine if a difference in the estimated proportions (PA − PB) reflects a difference in the population proportions.
  • The difference of two proportions follows an approximate normal distribution.
  • Generally, the null hypothesis states that the two proportions are the same.
  • To conduct the test, we use a pooled proportion, pc.

• Proportion and Scale

  • Proportion is a measurement of the size and quantity of elements within a composition.
  • Proportion is a measurement of the size and quantity of elements within a composition.
  • Hierarchical proportion is a technique used in art, mostly in sculpture and painting, in which the artist uses unnatural proportion or scale to depict the relative importance of the figures in the artwork.
  • Images of the human body in exaggerated proportion were used to depict the reality an artist interpreted.
  • Mathematically, proportion is the relation between elements and a whole.

• Estimating a Population Proportion

  • In order to estimate a population proportion of some attribute, it is helpful to rely on the proportions observed within a sample of the population.
  • As the size of a random sample increases, there is greater "confidence" that the observed sample proportion will be "close" to the actual population proportion.
  • In other words, with the larger sample size, it is generally apparent that the sample proportion will be closer to the actual "population" proportion of 50%.
  • While the sample proportion might be the best estimate of the total population proportion, you would not be very confident that this is exactly the population proportion.
  • The population proportion, $p$, is estimated using the sample proportion $\hat{p}$.

• Confidence Interval for a Population Proportion

  • $p'$ is the estimated proportion of successes ($p'$ is a point estimate for $p$, the true proportion)
  • The error bound for a proportion is seen in the formula in:
  • In the error bound formula, the sample proportions $p'$ and $q'$ are estimates of the unknown population proportions $p$ and $q$.
  • $p'$ is the estimated proportion of successes.
  • $q'$ is the estimated proportion of failures.

• Introduction to small sample hypothesis testing for a proportion

  • In this section we develop inferential methods for a single proportion that are appropriate when the sample size is too small to apply the normal model to ˆ p.

• The Law of Multiple Proportions

  • The law of multiple proportions states that elements combine in small whole number ratios to form compounds.
  • The law of multiple proportions, also known as Dalton's law, was proposed by the English chemist and meteorologist John Dalton in his 1804 work, A New System of Chemical Philosophy.
  • The law, which was based on Dalton's observations of the reactions of atmospheric gases, states that when elements form compounds, the proportions of the elements in those chemical compounds can be expressed in small whole number ratios.
  • Dalton's law of multiple proportions is part of the basis for modern atomic theory, along with Joseph Proust's law of definite composition (which states that compounds are formed by defined mass ratios of reacting elements) and the law of conservation of mass that was proposed by Antoine Lavoisier.

• Comparing Two Independent Population Proportions

  • Comparing two proportions (e.g., comparing two means) is common.
  • Generally, the null hypothesis states that the two proportions are the same.
  • To conduct the test, we use a pooled proportion, $p_c$.
  • Then $p_A$ and $p_B$ are the desired population proportions.
  • Demonstrate how a hypothesis test can help determine if a difference in estimated proportions reflects a difference in population proportions.

• Sample distribution of the difference of two proportions

  • First, the sampling distribution for each sample proportion must be nearly normal, and secondly, the samples must be independent.
  • where p 1 and p 2 represent the population proportions, and n 1 and n 2 represent the sample sizes.
  • The standard error for the difference in two proportions takes a similar form.

• Using Two Samples

  • To compare two means or two proportions, one works with two groups.
  • Politicians compare the proportion of individuals from different income brackets who might vote for them.
  • You will compare two means or two proportions to each other.
  • To compare two means or two proportions, one works with two groups.
  • The parameters tested using independent groups are either population means or population proportions.