Question

5. A certain production process produces 20 defective parts out of 200. An engineer designs a change in the process which results in 8 defective parts out of 200. Take a two-sided approach to answer the following questions. (a) 5 Do these data indicate that there is a difference in the support for decreasing pro- portion of defective parts due to changing the process? Find the P-value and report all relevant steps of the testing procedure. (b) Construct a 95% confidence interval on the difference in the two proportions of defective parts. alternative? (d) 5 Determine the sample size needed to detect this difference with a probability of at least 0.9. Use α-0.05.

Answer 1

riven data An Engineer cesigns change in pesse ark au Noll hypothesis f, r, Allende kral esic (+ ".: 80 200 8 800 mi 1-0.04 0-1(1-0.) o.04(1-004) 200 200 0.06 군 0-1(0,9) . 0.04(0.96) 20000 0.06 0.09 0.0384 200-t a00 o. OC Ο.OG 00004 o.00012.

2. __ o.oc 60.025333 Test statis-líc Zo 2.768 2- value of ailero p-value 0.01 5 level f Siqnificance0.05 f P- value < devel of Siqnifitane 0.017885 0.05 P-value < othesis (4 evidence-, someenl d,meme Gnclusion :--There is Werence In วา rz. 0-1(0.1) . о.оч(a96) 200 200 4 p-f e(o.ac) 1.95njo.coo6u 006)- 1.9599o.o00 41

R。p5tions of defective farls sample Sige needed -lo detel 4his dir.rna, unithap,obabil of atleaUse-o.05 2 0 左 ‘.out Z.

100-14) 0.1 0-0 2 7519 C12G) +1-2815 О.OG 1.9599↓0-1302 t 1.2815 Jo-las 4 o. 0036 !.9599(o. 3608 ) -t [.38IS (0.35833 0.0036 0-704132十0,459 19 0.0036 .IGG33092) 00036 I.3G 038 0.0036 =378