STAT 400 Lecture AL1 Examples for 8.1 (Part 1) Spring 2015 Dalpiaz Hypotheses Testing for the population mean Null Alternative H 0 : 0 vs. H 1 : < 0 Left - tailed. H 0 : 0 vs. H 1 : > 0 Right - tailed. H 0 : = 0 vs. H 1 : 0 Two - tailed. Test Statistic: n σμ0XZ OR ns 0μXT OR X Rejection Region: H 0 : 0 H 1 : < 0 Left - tailed. H 0 : 0 H 1 : > 0 Right - tailed. H 0 : 0 H 1 : 0 Two - tailed. Reject H 0 if Z < – z Reject H 0 if Z > z Reject H 0 if Z < – z /2 or Z > z /2 Reject H 0 if x < 0 – z n Reject H 0 if x > 0 + z n Reject H 0 if x < 0 – z /2 n or x > 0 + z /2 n 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: H 0 : vs. H 1 : Test Statistic: Rejection Region: Decision: P-value: 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. a) Perform the appropriate test. Use the significance level = 0.10. Claim: H 0 : vs. H 1 : Test Statistic: Rejection Region: Decision: P-value: 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 2.7873. 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 feet with the sample variance 16 feet 2. Perform the appropriate test. Claim: H 0 : vs. H 1 : Test Statistic: Rejection Region: Decision: P-value: 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
View Full Document