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Hypothesis Testing

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Hypothesis testing is a statistical process that involves making a tentative statement, called a hypothesis, about a population and then testing whether the available evidence supports or refutes that hypothesis.

Key Concepts:

  • Hypothesis: A statement that predicts the outcome of a study or experiment.
  • Null Hypothesis: A hypothesis that there is no difference or relationship between the variables being tested.
  • Alternative Hypothesis: A hypothesis that there is a difference or relationship between the variables being tested.
  • Test Statistic: A quantity calculated from the sample data that is used to assess the evidence against the null hypothesis.
  • P-value: The probability of obtaining the observed data or a more extreme data set under the assumption that the null hypothesis is true.
  • Significance Level: The pre-specified probability of Type I error (false positive).
  • Type I Error: Rejecting the null hypothesis when it is actually true.
  • Type II Error: Failing to reject the null hypothesis when it is actually false.

Steps:

  1. Formulate the Hypothesis: State the hypothesis you want to test.
  2. Collect Data: Gather data that is relevant to the hypothesis.
  3. Calculate the Test Statistic: Use statistical methods to calculate a test statistic based on the data.
  4. Determine the P-value: Calculate the probability of obtaining the observed test statistic or a more extreme statistic under the null hypothesis.
  5. Compare the P-value to the Significance Level: If the p-value is less than the significance level, reject the null hypothesis.
  6. Interpret the Results: Draw conclusions based on the results of the hypothesis test.

Example:

To test the hypothesis that the average height of women is 160 cm, you collect data from a sample of women and calculate the sample mean height. If the sample mean height is 162 cm and the p-value is less than the significance level of 0.05, you would reject the null hypothesis and conclude that the average height of women is greater than 160 cm.

Additional Notes:

  • Hypothesis testing is a formal statistical process, but it can be applied to a wide range of situations.
  • The choice of statistical test depends on the type of data and the hypothesis you want to test.
  • It is important to consider the sample size and the significance level when interpreting the results.

FAQs

  1. What is the 5% level of significance in hypothesis testing?

    The 5% level of significance (ฮฑ = 0.05) means there is a 5% chance of rejecting the null hypothesis when it is true. It is a common threshold used to determine whether the results of a test are statistically significant.

  2. What is a real-life example of hypothesis testing?

    A real-life example is testing whether a new medication is more effective than an existing one. The null hypothesis might state that there is no difference in effectiveness, while the alternative hypothesis states that the new medication is more effective. Data from clinical trials are used to test these hypotheses.

  3. What is a hypothesis test?

    A hypothesis test is a statistical method used to determine whether there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis based on sample data.

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