HYPOTHESIS TESTING:

Things to know

  1. Two areas of Inferential Statistics: Estimation and Hypothesis Testing.

  2. Hypothesis Testing is an area statistical inference in which one evaluates a conjecture about some characteristic of the population based upon the information contained in the random sample. Usually the conjecture concerns one of the unknown parameters of the population.

  3. Hypothesis is a claim or statement about the population parameter.

  4. Steps in Hypothesis Testing

    • State the null and alternative hypotheses.
    • Decide on a level of significance,
    • Select the appropriate test statistic.
    • Establish the critical region/regions.
    • Compute the actual value of the test statistic from the sample.
    • Make the statistical decision:
      • If decision rule is based on region of rejection: Check if test statistic falls in the region of rejection. If yes, reject the null hypothesis.
      • If decision rule is based on p-value: Determine the p-value. If the p-value is less than or equal to reject the null hypothesis.
    • Interpret results.

Example:

The mean weight of the sample of 100 persons from the Honolulu Heart Study is 63 kg. If the ideal weight is known to be 60 kg, is the group significantly overweight? Assume \(\sigma=0.05\) and \(\alpha=10kg.\)