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Hypothesis Tests

Hypothesis Tests. 2014/3/3. Purpose of hypothesis test. Hypothesis test is used to determine whether a statement about the value of of a population parameter should or should not be rejected. Ex. P.340 soft drink. Process of hypothesis test.

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Hypothesis Tests

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  1. Hypothesis Tests 2014/3/3

  2. Purpose of hypothesis test • Hypothesis test is used to determine whether a statement about the value of of a population parameter should or should not be rejected. • Ex. P.340 soft drink

  3. Process of hypothesis test • Step 1. Develop the null and alternative hypothesis. • Step 2. Specify the level of significance. • Step 3. Use the level of significance to determine the critical value and the rejection rule. • Step 4. Collect the sample data and compute the value of test statistic. • Step 5. Use the value of the test statistic and the rejection rule to determine whether to reject the null hypothesis.

  4. Process of hypothesis test • In step 1: • We begin by making a tentative assumption about a population parameter. This assumption is called the null hypothesis (H0). • We then define another hypothesis, called the alternative hypothesis (Ha), which is the opposite of what is stated in Ha. • The alternative hypothesis is often what the test is attempting to establish. • The equality part of the expression always appears in the null hypothesis. • Ex. P.340 Automobile model/Soft drink/ P. 351 Golf equipment

  5. Process of hypothesis test • In step 2 & step 3: • Determine α and rejection rule. • Assume H0 is right. If evidence does not support H0, we then reject H0. • Example. P 351. Golf equipment

  6. Process of hypothesis test • In step 4. • We first collect sample data. • We then compute the test statistic • Example P 351. Golf equipment

  7. Process of hypothesis test • In step 5: • We finally make a conclusion. • Example P 351. Golf equipment • Note. Two-tailed testing vs. one-tailed testing (P. 345 FTC example)

  8. P-value • The p-value is a probability that provides a measure of the evidence against the null hypothesis provided by the sample. • Smaller p-values indicate more evidence against H0. • Rejection rule using p-value: Reject H0 if p-value ≤α • Note. In two-tailed case, p-value = double the tail area.

  9. Test of population mean • Population mean: σ known • Population mean: σ unknown • Example. P.360

  10. Test of population proportion • Test statistic: • Example. P366. P.367.

  11. Test Error • Type I error: Pr(reject H0 | H0 true) = α • Type II error: Pr(accept H0 | Ha true) = β • Q. α + β = 1?

  12. Inferences About a Population Variance • Sampling distribution of (n - 1)s2/ 2 With 2 degrees of freedom With 5 degrees of freedom With 10 degrees of freedom 0

  13. Inferences About a Population Variance • Point estimator: • Interval estimator: (with n-1 degrees of freedom) • Hypothesis test: (with n-1 degrees of freedom)

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