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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.

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purpose of hypothesis test
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
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 test1
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 test2
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 test3
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 test4
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
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
Test of population mean
  • Population mean: σ known
  • Population mean: σ unknown
  • Example. P.360
test of population proportion
Test of population proportion
  • Test statistic:
  • Example. P366. P.367.
test error
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
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 variance1
Inferences About a Population Variance
  • Point estimator:
  • Interval estimator: (with n-1 degrees of freedom)
  • Hypothesis test: (with n-1 degrees of freedom)