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Recent coffee research

Hypothesis Testing. Recent coffee research. Hypothesis Testing. Recent coffee research. H 0 : p > 0.137. Coffee does not reduce the risk of diabetes. H a : p  < 0.137. Coffee reduces the risk of diabetes. Hypothesis Testing. H 0 : p  > 0.137.

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Recent coffee research

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  1. Hypothesis Testing Recent coffee research

  2. Hypothesis Testing Recent coffee research H0: p>0.137 Coffee does not reduce the risk of diabetes Ha: p<0.137 Coffee reduces the risk of diabetes

  3. Hypothesis Testing H0: p>0.137 Coffee does not reduce the risk of diabetes Ha: p<0.137 Coffee reduces the risk of diabetes H0: m=12 Subway’s FOOTLONG is a foot long Ha:m<>12 Subway’s FOOTLONG is not a foot long

  4. Hypothesis Testing one mean test—s known is normally distributed provided x is normally distributed ORx’s distribution is not heavily skewed and n > 30 ORx’s distribution is heavily skewed and n > 50 s 2 is some value that only Deity knows

  5. Hypothesis Testing one mean test—s known one mean test—s unknown is normally distributed provided x is normally distributed ORx’s distribution is not heavily skewed and n > 30 ORx’s distribution is heavily skewed and n > 50 What do you do if Deity won’t reveal to you the value of s 2?

  6. Hypothesis Testing one mean test—s unknown The t distribution is the exact distribution if x is normally distributed What do you do if Deity won’t reveal to you the value of s 2?

  7. Hypothesis Testing one mean test—s unknown The t distribution is the approximatedistribution if x is normally distributed ORn > 30 and x is NOT heavily skewed ORn > 50 and x is HEAVILY skewed What do you do if Deity won’t reveal to you the value of s 2?

  8. Hypothesis Testing one proportion test is approximately normally distributed if np0 > 5 and n (1–p0) > 5 What do you use for s 2 when you test a proportion?

  9. Hypothesis Testing • 1960s Chips Ahoy cookie TV commercial claim

  10. Hypothesis Testing The null hypothesis is assumed to be true H0: = 16 the cookies have 16 chips Rejecting a true H0 is a Type I error The sample says the cookies do not have 16 chips when they actually do. This error is costly because the production line will be shutdown to fix a problem that does not exist

  11. Hypothesis Testing The alternative hypothesis is the opposite H0: = 16 the cookies have 16 chips Ha:  < > 16 the cookies do not have 16 chips Rejecting a true H0 is a Type I error Rejecting a true Ha is a Type II error The sample says the cookies have 16 chipswhen they really do not. The error will upset Chips Ahoy’s customers if there are too few OR increase Chips Ahoy’s costs if there are too many

  12. Hypothesis Testing The alternative hypothesis is the opposite H0: = 16 the cookies have 16 chips Ha:  < > 16 the cookies do not have 16 chips Rejecting a true H0 is a Type I error Rejecting a true Ha is a Type II error What conclusion is appropriate when H0 is rejected?

  13. Hypothesis Testing The alternative hypothesis is the opposite H0: = 16 the cookies have 16 chips We cannot conclude that Ha:  < > 16 the cookies do not have 16 chips Rejecting a true H0 is a Type I error Rejecting a true Ha is a Type II error What conclusion is appropriate when H0 cannot be rejected?

  14. Hypothesis Testing Example: Chips Ahoy Chocolate Chip Cookies one mean test—s unknown Perform a hypothesis test, at the 5% level of significance, to determine if Chips Ahoy cookies have an average of 16 chips per cookie. proportion test mean test mean test s 2 known s 2 = p0(1 – p0)

  15. Hypothesis Testing one mean test—s unknown

  16. Hypothesis Testing one mean test—s unknown 1. Determine the hypotheses. H0: m = 16 Ha: m < > 16 2. Compute the test statistic

  17. Hypothesis Testing one mean test—s unknown 3. Determine the critical value(s). Ha: m < > 16 a = .050 a/2 = .025 df = 30 – 1 = 29

  18. Hypothesis Testing one mean test—s unknown 3. Determine the critical value(s). Ha: m < > 16 a = .050 -t.0250 = -2.045 t.0250 = 2.045

  19. Hypothesis Testing one mean test—s unknown 4. Conclude Do Not Reject H0: =16 .025 .025 t 1.91t-stat 0 -2.045 2.045 We cannot conclude that the cookies do not have 16 chips

  20. Hypothesis Testing one proportion test Example: National Safety Council (NSC) The National Safety Council claimed that more than 50% of the accidents are caused by drunk driving. A sample of 120 accidents showed that 67 were caused by drunk driving. Perform a hypothesis test, at the 2.5% level of significance, to determine if NSC’s claim is valid.

  21. Hypothesis Testing one proportion test 1. Determine the hypotheses. 2. Compute the test statistic

  22. Hypothesis Testing one proportion test 3. Determine the critical value(s). a/1=.0250 a = .0250 Ha: p> .5 -z.0250 ≈ -1.96 z.0250 ≈ 1.96

  23. Hypothesis Testing one proportion test 4. Conclude Do Not Reject H0: p< .5 .025 z 1.28 z-stat 0 1.96 We cannotconclude that more than 50% of accidents are caused by drunk driving

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