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Recent coffee research Hypothesis Testing

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

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Subways FOOTLONG is not a foot long Subways FOOTLONG is a foot long H 0 : = H a : Hypothesis Testing Coffee reduces the risk of diabetes H a : p < Coffee does not reduce the risk of diabetes H 0 : p >

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

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is normally distributed provided x is normally distributed one mean test known Hypothesis Testing What do you do if Deity wont reveal to you the value of 2 ? one mean test unknown OR x s distribution is not heavily skewed and n > 30 OR x s distribution is heavily skewed and n > 50

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The t distribution is the exact distribution if one mean test unknown Hypothesis Testing x is normally distributed What do you do if Deity wont reveal to you the value of 2 ?

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x is normally distributed The t distribution is the approximate distribution if OR n > 30 and x is NOT heavily skewed OR n > 50 and x is HEAVILY skewed one mean test unknown Hypothesis Testing What do you do if Deity wont reveal to you the value of 2 ?

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one proportion test is approximately normally distributed if n p 0 > 5 and n (1 p 0 ) > 5 Hypothesis Testing What do you use for 2 when you test a proportion?

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1960s Chips Ahoy cookie TV commercial claim Hypothesis Testing

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the cookies have 16 chips H 0 : = 16 Hypothesis Testing The null hypothesis is assumed to be true 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 Rejecting a true H 0 is a Type I error

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the cookies have 16 chips H 0 : = 16 Hypothesis Testing Rejecting a true H 0 is a Type I error Rejecting a true H a is a Type II error The alternative hypothesis is the opposite The sample says the cookies have 16 chips when they really do not. The error will upset Chips Ahoys customers if there are too few OR increase Chips Ahoys costs if there are too many the cookies do not have 16 chips H a : 16

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The alternative hypothesis is the opposite Rejecting a true H 0 is a Type I error is rejected? Hypothesis Testing Rejecting a true H a is a Type II error What conclusion is appropriate when H 0 the cookies have 16 chips H 0 : = 16 the cookies do not have 16 chips H a : 16

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The alternative hypothesis is the opposite cannot be rejected? Hypothesis Testing Rejecting a true H 0 is a Type I error Rejecting a true H a is a Type II error What conclusion is appropriate when H 0 the cookies do not have 16 chips H a : 16 the cookies have 16 chips H 0 : = 16 We cannot conclude that

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

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Bottle Number of Chips deviation from mean 114 -2.5 215 -1.5 315 -1.5 417 0.5 518 1.5 616 -0.5 715 -1.5 2919 2.5 3017 0.5 Total495 0 one mean test unknown Hypothesis Testing

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1. Determine the hypotheses. H a : 16 2. Compute the test statistic one mean test unknown Hypothesis Testing H 0 : = 16

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degrees of freedom.200.100.050.025.010.005 28.8551.3131.7012.0482.4672.763 29.8541.3111.6992.0452.4622.756 30.8541.3101.6972.0422.4572.750 31.8531.3091.6962.0402.4532.744 32.8531.3091.6942.0372.4492.738 33.8531.3081.6922.0352.4452.733 34.8521.3071.6912.0322.4412.728 df = 30 1 = 29 =.050 /2 =.025 H a : 16 one mean test unknown 3. Determine the critical value(s). Hypothesis Testing

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degrees of freedom.200.100.050.025.010.005 28.8551.3131.7012.0482.4672.763 29.8541.3111.6992.0452.4622.756 30.8541.3101.6972.0422.4572.750 31.8531.3091.6962.0402.4532.744 32.8531.3091.6942.0372.4492.738 33.8531.3081.6922.0352.4452.733 34.8521.3071.6912.0322.4412.728 t.0250 = 2.045 -t.0250 = -2.045 one mean test unknown 3. Determine the critical value(s). Hypothesis Testing =.050 H a : 16

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-2.045 2.045.025 1.91 t-stat 0 t.025 Do Not Reject H 0 : 4. Conclude the cookies do not have 16 chips We cannot conclude that one mean test unknown Hypothesis Testing

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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 NSCs claim is valid. one proportion test Hypothesis Testing

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

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Z.00.01.02.03.04.05.06.07.08.09 -2.2.0139.0136.0132.0129.0125.0122.0119.0116.0113.0110 -2.1.0179.0174.0170.0166.0162.0158.0154.0150.0146.0143 -2.0.0228.0222.0217.0212.0207.0202.0197.0192.0188.0183 -1.9.0287.0281.0274.0268.0262.0256.0250.0244.0239.0233 -1.8.0359.0351.0344.0336.0329.0322.0314.0307.0301.0294 -1.7.0446.0436.0427.0418.0409.0401.0392.0384.0375.0367 H a : p >.5 =.0250 / 1 =.0250 one proportion test 3. Determine the critical value(s). Hypothesis Testing -z.0250 -1.96 z.0250 1.96

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1.96 1.28 z-stat 0 z.025 H 0 : p