INDU 6331 Assignment 3 Advanced Quality Control

4.1 The inside diameters of bearings used in an aircraft landing gear assembly are known to have a standard deviation of σ= 0.002cm. A random sample of 15 bearings has an average inside diameter of 8.2535cm a. Test the hypothesis that the mean inside bearing diameter is 8.25cm Use a two-sided alternative and α= 0.05 σ= 0.002 n= 15 Samp. aveg.= 8.2535 α= 0.05 H0: μ0= 8.25 H1: μ0≠ 8.25 Zα /2=Z0.025=1.96 Zo= x´−μ0 σ /√n = 8.2535−8.25 0.002/√15 =6.77 If /Z0/ Zα/2  Reject H0 6.77 1.96  Rejected With a 95% confidence level we can reject H0. We can assume that the mean inside bearing diameter is not 8.25cm b. Find the P-value for this test P−value=[1−Φ( Z0) ]∗2=¿ [ 1−Φ(6.77 )]∗2≈ 0.000 For this test the P-value is less than 0.000 . Any level of significance greater than 0.000 would let to rejection of H0 c. Construct a 95% two sided confidence interval on mean bearing diameter ´x−Zα 2 σ √n ≤μ≤ ´x+Zα/ 2 σ √n 8.2535− 1.96∗0.002 √15 ≤ μ≤ 8.2535+ 1.96∗0.002 √15 INDU 6331 Assignment 3 Advanced Quality Control 8.2525≤μ≤8.2545 The estimate of mean bearing diameter is between 8.2525cm and 8.2545cm with a confidence level of 95% 4.2 The tensile strength of a fiber using in manufacturing cloth is of interest to the purchaser. Previous experience indicates that the standard deviation of tensile strength is 2psi. A random sample of eight fiber specimens is selected, and the average tensile strength is found to be 127psi a. Test the hypothesis that the mean tensile strength equals 125psi versus the alternative that the mean exceeds 125psi. Use α= 0.05 σ= 2 n= 8 Samp. aveg.= 127 α= 0.05 H0: μ0= 125 H1: μ0 125 Zα=Z0.05=1.64 Zo= x´−μ0 σ /√n = 127−125 2/√8 =2.828 If Z0 Zα  Reject H0 2.828 1.64  Rejected With 95% confidence level we can reject H0. It can be assumed that the mean tensile strength exceeds 125psi b. What is the P-value for this test?