hypothesis

Examples of hypothesis in the following topics:

• Student Learning Outcomes

  • Conduct and interpret hypothesis tests for two population means, population standard deviations known.
  • Conduct and interpret hypothesis tests for two population means, population standard deviations unknown.

• The Null and the Alternative

  • The alternative hypothesis and the null hypothesis are the two rival hypotheses that are compared by a statistical hypothesis test.
  • In statistical hypothesis testing, the alternative hypothesis and the null hypothesis are the two rival hypotheses which are compared by a statistical hypothesis test.
  • In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis, and these are decided between on the basis of data, with certain error rates.
  • The concept of an alternative hypothesis forms a major component in modern statistical hypothesis testing; however, it was not part of Ronald Fisher's formulation of statistical hypothesis testing.
  • Modern statistical hypothesis testing accommodates this type of test, since the alternative hypothesis can be just the negation of the null hypothesis.

• Does the Difference Prove the Point?

  • Rejecting the null hypothesis does not necessarily prove the alternative hypothesis.
  • The critical region of a hypothesis test is the set of all outcomes which cause the null hypothesis to be rejected in favor of the alternative hypothesis.
  • Alternatively, if the testing procedure forces us to reject the null hypothesis ($H_0$), we can accept the alternative hypothesis ($H_1$) and we conclude that the research hypothesis is supported by the data.
  • Rejection of the null hypothesis is a conclusion.
  • We might accept the alternative hypothesis (and the research hypothesis).

• Student Learning Outcomes

  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.
  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.

• Student Learning Outcomes

• Misconceptions

  • State why the probability value is not the probability the null hypothesis is false
  • Explain why a non-significant outcome does not mean the null hypothesis is probably true
  • Misconception: The probability value is the probability that the null hypothesis is false.
  • It is the probability of the data given the null hypothesis.
  • It is not the probability that the null hypothesis is false.

• Steps in Hypothesis Testing

  • Be able to state the null hypothesis for both one-tailed and two-tailed tests
  • The first step is to specify the null hypothesis.
  • A typical null hypothesis is μ1 - μ2 = 0 which is equivalent to μ1 = μ2.
  • If the probability value is lower then you reject the null hypothesis.
  • Failure to reject the null hypothesis does not constitute support for the null hypothesis.

• Formulating the Hypothesis

  • A hypothesis is a potential answer to your research question; the research process helps you determine if your hypothesis is true.
  • This is an example of a causal hypothesis.
  • To test this hypothesis, he compared twenty different regional Italian governments.
  • To test this hypothesis, he compared twenty different regional Italian governments.
  • While there is no single way to develop a hypothesis, a useful hypothesis will use deductive reasoning to make predictions that can be experimentally assessed.

• Type I and II Errors

  • Explain why the null hypothesis should not be accepted when the effect is not significant
  • Instead, α is the probability of a Type I error given that the null hypothesis is true.
  • If the null hypothesis is false, then it is impossible to make a Type I error.
  • Lack of significance does not support the conclusion that the null hypothesis is true.
  • A Type II error can only occur if the null hypothesis is false.

• Elements of a Hypothesis Test

  • The null hypothesis was that the Lady had no such ability.
  • Fisher asserted that no alternative hypothesis was (ever) required.
  • Statistical hypothesis tests define a procedure that controls (fixes) the probability of incorrectly deciding that a default position (null hypothesis) is incorrect based on how likely it would be for a set of observations to occur if the null hypothesis were true.
  • The typical line of reasoning in a hypothesis test is as follows:
  • There is an initial research hypothesis of which the truth is unknown.