Hypothesis Test for one Sample

Hypothesis Test for one Sample

1. Hypothesis test

   • A hypothesis test (or test of significance) is a standard procedure for testing a claim about a parameter of a population.
   • Components of Hypothesis Test
     • Null hypothesis
       • The null hypothesis (denoted by H0 ) is a statement that the value of a population parameter (such as proportion, mean, or standard deviation) is:
     • Alternative hypothesis
       • The alternative hypothesis (denoted by H1 or Ha or HA ) is the statement that the parameter has a value that somehow differs from the null hypothesis
         • An alternative hypothesis is a complimentary event of a null hypothesis
         • The symbolic form of the alternative hypothesis must use one of these symbols: ≠, <, >.
     • Significance level
       • Significance level (denoted by a) of a test is the probability that the test statistic will fall in the critical region when the null hypothesis is actually true.
       • If the test statistic falls in the critical region, we reject the null hypothesis, so it is the probability of making the mistake of rejecting the null hypothesis when it is true.
     • A random sample has to come up with a test statistics to make a decision of either rejecting or failing to reject H0
     • Test statistic
       • The test statistic is a value used in decision making process for the null hypothesis and it is found by converting the sample statistic to a score with the assumption that the null hypothesis is true.
       • Test statistic for proportion
       • Test statistic for mean
       • Critical value
         • A critical value is the value that separates the critical region (where we reject the null hypothesis) from the values of the test statistic that do not lead to rejection of the null hypothesis.
         • The critical value depends on the nature of the null hypothesis, the sampling distribution that applies, and the significance level .
       • Critical region
         • The critical region (or rejection region) is the set of all values of the test statistic that cause to reject the null hypothesis.
         • The critical region is determined by significance level for a test.

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