alternative hypothesis

Examples of alternative hypothesis in the following topics:

• 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 case of a scalar parameter, there are four principal types of alternative hypothesis:
  • Point alternative hypotheses occur when the hypothesis test is framed so that the population distribution under the alternative hypothesis is a fully defined distribution, with no unknown parameters.
  • 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).

• Hypothesis testing framework

  • We call H 0 the null hypothesis and H A the alternative hypothesis.
  • The alternative hypothesis (H A ) represents an alternative claim under consideration and is often represented by a range of possible parameter values.
  • The alternative hypothesis often represents a new perspective, such as the possibility that there has been a change.
  • If we set these claims up in a hypothesis framework, which would be the null hypothesis and which the alternative?
  • Failing to find strong evidence for the alternative hypothesis is not equivalent to accepting the null hypothesis.

• Decision and Conclusion

  • A systematic way to make a decision of whether to reject or not reject the null hypothesis is to compare the p-value and a preset or preconceived α (also called a "significance level").
  • A preset α is the probability of a Type I error (rejecting the null hypothesis when the null hypothesis is true).
  • There is sufficient evidence to conclude that Ho is an incorrect belief and that the alternative hypothesis, Ha, may be correct.
  • There is not sufficient evidence to conclude that the alternative hypothesis, Ha, may be correct.

• Testing a Single Proportion

  • Hypotheses: State the null and alternative hypotheses in words then in symbolic form:
  • Null Hypothesis in words: The null hypothesis is that the true population proportion of households that own at least three cell phones is equal to 30%.
  • Alternative Hypothesis in words: The alternative hypothesis is that the population proportion of households that own at least three cell phones is more than 30%.
  • The conditions are satisfied, so we will use a hypothesis test for a single proportion to test the null hypothesis.
  • Calculate and display your confidence interval for the alternative hypothesis.

• Null and Alternate Hypotheses

  • They are called the null hypothesis and the alternate hypothesis.
  • Ha: The alternate hypothesis: It is a claim about the population that is contradictory to Ho and what we conclude when we reject Ho.
  • Since the null and alternate hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not.
  • They are "reject Ho" if the sample information favors the alternate hypothesis or "do not reject Ho" or "fail to reject Ho" if the sample information is insufficient to reject the null hypothesis.
  • The choice of symbol depends on the wording of the hypothesis test.

• Using the Sample to Test the Null Hypothesis

  • We would reject the null hypothesis if the evidence is strongly against it.
  • The null hypothesis could be Ho: µ ≤15 The alternate hypothesis is Ha: µ > 15
  • The words "is more than" translates as a "> " so "µ > 15" goes into the alternate hypothesis.
  • The null hypothesis must contradict the alternate hypothesis.
  • The hypothesis test works by asking the question how unlikely the sample mean would be if the null hypothesis were true.

• Interpreting Significant Results

  • If the null hypothesis is rejected, then the alternative to the null hypothesis (called the alternative hypothesis) is accepted.
  • If this null hypothesis is rejected, then the alternative hypothesis that π > 0.5 is accepted.
  • The null hypothesis is:
  • If this null hypothesis is rejected, then there are two alternatives:
  • Naturally, the direction of the sample means determines which alternative is adopted.

• Elements of a Hypothesis Test

  • Fisher asserted that no alternative hypothesis was (ever) required.
  • Note that this probability of making an incorrect decision is not the probability that the null hypothesis is true, nor whether any specific alternative hypothesis is true.
  • This contrasts with other possible techniques of decision theory in which the null and alternative hypothesis are treated on a more equal basis.
  • Decide to either reject the null hypothesis in favor of the alternative or not reject it.
  • Reject the null hypothesis in favor of the alternative or not reject it.

• Testing a Single Mean

  • He performs a hypothesis test using a 5% level of significance.
  • Hypotheses: State the null and alternative hypotheses in words and then in symbolic form Express the hypothesis to be tested in symbolic form.
  • The alternative hypothesis is the statement without the equality.
  • Null hypothesis in words: The null hypothesis is that the true mean of the statistics exam is equal to 65.
  • Alternative hypothesis in words: The alternative is that the true mean statistics score on average is less than 65.