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# 101011u - AGENDA Hypotheses concerning one mean Hypotheses...

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Sheet1 Page 1 AGENDA Hypotheses concerning one mean Hypotheses concerning two means EXAMPLE 2 Claimed tire lifetime of at least 28,000 miles is suspect Sample 40 tires Mean=27,463 Std=1,348 Conclusions at an alpha level = 0.05? APPROACH Interested in if the lifetime is <28,000 miles One sided test Known mean, unknown variance Sample size is >30 Use Z test, but substitute sigma with s STEP 1HYPOTHESES Ho: The mean u is greater than or equal to 28,000 Ha: The mean is less than 28,000 STEP 2DETERMINE LEVEL OF SIGNIFICANCE STEP 3DETERMINE CRITICAL VALUE Use Z table to obtain °critical value° for alpha=0.01 STEP 4CALCULATIONS Use formula for Z distribution Z=-2.52 STEP 5DECISION Critical value =-2.33 Test statistic = -2.52 Test statistic is less than critical value Reject Ho English There is evidence to support the claim that the tires have a lifetime of less than 28,000 at an alpha level of 0.01 EXAMPLE 3 Specs of ribbon require mean breaking strength of 180 pounds Sample 5 observations Mean is 169.5 pounds Std is 5.7 pounds Ho and Ha are given Significance level of 0.01

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Sheet1 Page 2 Assume normality APPROACH Concern about mean breaking strength being less than 180 pounds One sided test Known mean, unknown variance Sample size is < 30 STEP 1HYPOTHESES Ho: The mean u is greater than or equal to 180 Ha: The mean is less than 180 STEP 2DETERMINE LEVEL OF SIGNIFICANCE STEP 3DETERMINE CRITICAL VALUE Use t table to obtain °critical value° for alpha=0.01, 4 degrees of freedom STEP 4CALCULATIONS Use formula for t distribution T= -4.12 STEP 5DECISION Critical value =-3.747
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101011u - AGENDA Hypotheses concerning one mean Hypotheses...

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