5. [-10.3 Points] DETAILS DEVORESTATQ 8.SE.080.S. MY NOTES ASK YOURTEACHER PRACTICE ANOTHER Because of variability in the manufacturing process, the actual yielding point of a sample of mild steel subjected to Increasing stress will usually differ from the theoretical yielding point. Letp denote the true proportion of samples that yield before their theoretical yielding point. If on the basis of a sample it can be concluded that more than 20% of all specimens yield before the theoretical point, the production process will have to be modified. Open SALT in a new tab (a) If 13 of 48 specimens yield before the theoretical point, what is the Pvalue when the appropriate testis used? (Round your answer to four decimal places.) What would you adVise the company to do? 0 Because the P-value is rather small, HEl will be rejected at any reasonable 0:, so no modication appears necessary. 0 Because the Pyalue ls rather large, HO would not be rejected at any reasonable 1, so no modification appears necessary. 0 Because the P-value ls rather small, H will be reacted at any reasonable at, so the production process will have to be modied. 3 J 0 Because the P-value is rather large, H0 would not be rejected at any reasonable a, so the production process Wlll have to be modied. (b) If the true percentage of "early yields" is actually 50% (so that the theoretical point is the median of the yield distribution) and a level 0.01 test is used, what is the probability that the company concludes a modification of the process is necessary? (Round your answer to four decimal places.) Z You may need to use the appropriate table in the Appendix ofTables to answer this