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Hypothesis Tests

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# Hypothesis Tests - PowerPoint PPT Presentation

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

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
• 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.
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
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
Process of hypothesis test
• In step 4.
• We first collect sample data.
• We then compute the test statistic
• Example P 351. Golf equipment
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)
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.
Test of population mean
• Population mean: σ known
• Population mean: σ unknown
• Example. P.360
Test of population proportion
• Test statistic:
• Example. P366. P.367.
Test Error
• Type I error:

Pr(reject H0 | H0 true) = α

• Type II error:

Pr(accept H0 | Ha true) = β

• Q. α + β = 1?
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

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