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10.2 – Tests of Significance

10.2 – Tests of Significance. Reasoning. Suppose null hypothesis is true. Usually that there is no change or no effect in the population If we were to repeat our sampling numerous times, what would the chances be that we would observe a sample value as extreme as the one that was observed?.

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10.2 – Tests of Significance

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  1. 10.2 – Tests of Significance

  2. Reasoning • Suppose null hypothesis is true. • Usually that there is no change or no effect in the population • If we were to repeat our sampling numerous times, what would the chances be that we would observe a sample value as extreme as the one that was observed?

  3. P-Value • The probability of a result at least as far out as the results we actually got. • The lower the value, the more surprising out result, and the stronger evidence against the null hypothesis. • A result with a low p-value (ex less than 0.05) is called statistically significant • Significance level – the decisive value of P. Termed alpha: α. When p < α, the result is statistically significant.

  4. Hypotheses • Ho: the null hypothesis: the statement being tested. • Usually a statement of no effect or no difference • Ha: the alternative hypothesis: the claim about the population that we are trying to find evidence for. • One-sided or two sided.

  5. Steps to a Significance Tests • Identify the population of interest and the parameter you want to draw conclusions about. State the null and alternative hypotheses in words and symbols. • Choose the appropriate inference procedure. Verify the conditions for using the procedure. • If the conditions are met, carry out the inference procedure. • Calculate the test statistic • Find the P-value • Interpret your results in the context of the problem.

  6. Z- Test for a Population Mean • To test the hypothesis Ho: μo = μ based on a SRS of size n from a population with unknown mean μ and known standard deviation σ, compute a one-sample z statistic: • In terms of a variable Z having the standard normal distribution, the P-value for a test of Ho against:

  7. Alternative Hypotheses • Ha: μ > μo is P(Z > z) • Ha: μ < μo is P(Z < z) • Ha: μ = μo is 2P(Z > |z|)

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