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CHAPTER 9

CHAPTER 9. STATISTICAL HYPOTHESIS TESTING: HYPOTHESIS TESTS FOR A POPULATION MEAN. The Nature of Hypothesis Testing.

jileen-caffrey
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CHAPTER 9

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  1. CHAPTER 9 STATISTICAL HYPOTHESIS TESTING:HYPOTHESIS TESTS FOR A POPULATION MEAN

  2. The Nature of Hypothesis Testing • In hypothesis testing, a statement—call it a hypothesis— is made about some characteristic of a particular population. A sample is then taken in an effort to establish whether or not the statement is true. • If the sample produces a result that would be highly unlikely under an assumption that the statement is true, then we’ll conclude that the statement is false.

  3. Choosing the Null Hypothesis • The status quo or “if-it’s-not-broken-don’t-fix-it” approach • The good sport approach • The skeptic’s “show me” approach

  4. Standard Forms for the Null and Alternative Hypotheses H0: m> A (The population mean is greater than or equal to A) Ha: m < A (The population mean is less than A) H0: m< A(The population mean is less than or equal to A) Ha: m > A(The population mean is greater than A) H0: m = A(The population mean is equal to A) Ha: m ≠ A(The population mean is not equal to A)

  5. m Figure 9.1 The Sampling Distribution of the Sample Mean s =

  6. Figure 9.2 The “Null” Sampling Distributionm = 5000 m =5000

  7. Figure 9.3 Likely and Unlikely Sample Means in the “Null” Sampling Distribution m = 5000 = 5 = 4997 = 4998

  8. Significance Level (a) A significance level defines what we mean by unlikely sample results under an assumption that the null hypothesis is true (as an equality).

  9. REJECT H0 pounds scale a= .05 x m= 5000 z scale zc = -1.65 0 Figure 9.4 Setting the Boundary on the “Null” Sampling Distribution z

  10. REJECT H0 pounds scale = 4912 m= 5000 z scale zc = -1.65 0 Figure 9.5 Showing zstaton the Null Sampling Distribution zstat= -2.49 z

  11. The Four Steps of Hypothesis Testing Step 1: State the null and alternative hypotheses. Step 2: Choose a test statistic and use the significance level to establish a decision rule. Step 3: Compute the value of the test statistic. Step 4: Apply the decision rule and make your decision.

  12. REJECT H0 pounds scale a=.05 c = 4941.6 m= 5000 z scale z zc = -1.65 0 Figure 9.6 Showing the Boundary, c, on the Null Sampling Distribution

  13. p-value The p-value measures the probability that, if the null hypothesis were true, we would randomly produce a sample result at least as unlikely as the sample result we actually produced.

  14. p-value = .1423 .3577 (pounds) 5000 4962 z -1.07 Figure 9.7 p-value for a Sample Mean of 4962 0

  15. p-value Decision Rule If the p-value is less than , reject the null hypothesis.

  16. REJECT H0 p-value = .1423 4941.6 4962 5000 (pounds) a = .05 z 0 zc = -1.65 zstat =-1.07 Figure 9.8 Using the p-value to Make a Decision

  17. Error Possibilities in Hypothesis Testing TYPE I Error: Rejecting a true null hypothesis. TYPE II Error: Accepting a false null hypothesis.

  18. a and the Risk of Type I Error a measures the maximum probability of making a Type I Error.

  19. REJECT H0 REJECT H0 a /2 a/2 m z 0 zcu zcl Figure 9.9 A Two-tailed Hypothesis Test

  20. REJECT H0 REJECT H0 a/2 = .025 a/2 = .025 cL = 4930.7 5000 cu = 5069.3 z -1.96 0 +1.96 Figure 9.10 A Two-tailed Hypothesis Test for Montclair Motors

  21. Test Statistic When s Replaces s (9.2) tstat=

  22. REJECT H0 a = .05 t 0 tc= -1.761 tstat = -1.37 Figure 9.11 Testing with the t Distribution

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