STAT 400 Lecture AL1 Spring 2015 Dalpiaz Examples for 8 1 Part 1 Hypotheses Testing for the population mean Null Alternative H0 0 vs H1 0 Left tailed H0 0 vs H1 0 Right tailed H0 0 vs H1 0 Two tailed Z Test Statistic X 0 OR n T X 0 s OR n Rejection Region H0 0 H0 0 H0 0 H1 0 H1 0 H1 0 Left tailed Right tailed Two tailed Reject H 0 if Reject H 0 if Reject H 0 if Z z Z z 2 Z z or Z z 2 Reject H 0 if Reject H 0 if x 0 z Reject H 0 if n x 0 z n x 0 z 2 n or x 0 z 2 n X 1 The overall standard deviation of the diameters of the ball bearings is 0 005 mm The overall mean diameter of the ball bearings must be 4 300 mm A sample of 81 ball bearings had a sample mean diameter of 4 299 mm Is there a reason to believe that the actual overall mean diameter of the ball bearings is not 4 300 mm a Perform the appropriate test using a 10 level of significance Claim H0 vs H1 Test Statistic Rejection Region P value Decision Decision Confidence Interval Decision b State your decision Accept H 0 or Reject H 0 for the significance level 0 05 2 A trucking firm believes that its mean weekly loss due to damaged shipments is at most 1800 Half a year 26 weeks of operation shows a sample mean weekly loss of 1921 54 with a sample standard deviation of 249 39 Perform the appropriate test Use the significance level 0 10 a Claim H0 H1 vs Test Statistic Rejection Region P value Decision Decision b State your decision Accept H 0 or Reject H 0 for the significance level 0 05 The t Distribution r t 0 40 t 0 25 t 0 20 t 0 15 t 0 10 t 0 05 t 0 025 t 0 02 t 0 01 t 0 005 25 0 256 0 684 0 856 1 058 1 316 1 708 2 060 2 167 2 485 2 787 3 Metaltech Industries manufactures carbide drill tips used in drilling oil wells The life of a carbide drill tip is measured by how many feet can be drilled before the tip wears out Metaltech claims that under typical drilling conditions the life of a carbide tip follows a normal distribution with mean of at least 32 feet Suppose some customers disagree with Metaltech s claims and argue that Metaltech is overstating the mean i e the mean is actually less than 32 Metaltech agrees to examine a random sample of 25 carbide tips to test its claim against the customers claim If the Metaltech s claim is rejected Metaltech has agreed to give customers a price rebate on past purchases Suppose Metaltech decided to use a 5 level of significance and the observed sample mean is 30 5 2 feet with the sample variance 16 feet Perform the appropriate test Claim H0 H1 vs Test Statistic Rejection Region P value Decision Decision The t Distribution r t 0 40 t 0 25 t 0 20 t 0 15 t 0 10 t 0 05 t 0 025 t 0 02 t 0 01 t 0 005 24 0 256 0 685 0 857 1 059 1 318 1 711 2 064 2 172 2 492 2 797
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