Solutions to Ma381, Exam 3 (blue version), F04.

# Solutions to Ma381, Exam 3 (blue version), F04. - Problem...

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Unformatted text preview: Problem A. (40 pts.) Suppose electrical resistors stated to have 100 ohms meet speciﬁcations if they are within 2 ohms of this amount. Also suppose management has expressed a concern that the true proportion of resistors not meeting speciﬁcations has increased from the historical level of 10%. A random sample of 180 resistors yields 25 having resistances that don’t meet speciﬁcations. In what follows on pages 2-3, let p = Proportion of resistors not meeting speciﬁcations 1. Give a point estimate for p. M= 5.3.. 2. Give a 95% conﬁdence interval for p. fir/.9; WP?) \$60879 JPN) 3. Conduct the appropriate hypothesis test with signiﬁcance level a: 0.05: a. State the hypotheses corresponding to the concern of management Ho: p3,! I / HA: f)" b. State the decision rule for a signiﬁcance level of a = 0.05. A- 1"? u 7 /.é¢5/ Mrﬁaﬂ' Ho m V? A .3? f1 4 (15/ 41"» 466%KD (Kr-e ’— m c. Compute the relevant test statistic. , E) ll ? 5R: l H? 3 w .9 d. Come to a decision about which hypothesis you believe. Lbla- Ca) 7) ﬂmC'f‘Ho e. The testing procedure for this problem makes use of the Central Limit Theorem. Show me that the necessary condition(s) for this procedure to be valid are satisﬁed. (8” = lo‘OC-l) 5-‘MVZ/D [62. g [may == may) a ,0 / Problem B. (40 pts.) The Charpy V-notch impact test is the basis for studying many material toughness criteria. This test was applied to 45 samples of a particular alloy at a given temperature. The sample average amount of transverse lateral expansion was computed to be 52.2 mils, and the sample standard deviation was s = 7.3 mils. To be suitable for a particular application, the true average amount of expansion should be less than 55 mils. The alloy will not be used unless the sample provides compelling evidence that this criterion has «been met. In what follows on pages 4—5, let u = True average transverse lateral expansion 1. Give a point estimate for y. ~ “- M = a? 5mm; 2. Give a 95% conﬁdence interval for ,u. .. 5 7.3 321.16 \7’5 , 52.2:t 1.74 ff; (50.06; 57.33;) ll! 3. Conduct the appropriate hypothesis test with signiﬁcance level a = 0.01: a. State the hypotheses corresponding to the concern of management Ho: ’61 =5; / HA: [(455 b. State the decision rule for a signiﬁcance level of a = 0.01. ff :3“ ( v2.33, rm. r946" ”0 97w: d. Come to a decision about which hypothesis you believe. e. The testing procedure for this problem makes use of the Central Limit Theorem. Show me that the necessary condition(s) for this procedure to be valid are satisﬁed. m=+52 in foE: Exm— mm (WM/‘Cp Fm) (”ML B/AréW/m J's .7é?H~ (77 FM; Mam; 0/5173) \ Problem C. (20 pts) Suppose, in problem A (involving the resistors), that the actual percentage of N5. 5hr; Animators not meeting speciﬁcations is 10%. For a random sample of 180 resistors, estimate the chance that we have 15, 16, 17, . . ., or 25 resistors that do not meet speciﬁcations using the Central Limit Theorem. Bonus points for correctly using the continuity correction (or “split-the- , difference”) method. W: M 25> N Mme»; (80 {59 If A 3.5. .. "V(K5”" < I7“? lip " — 1 (.1932 1’01”) " @120?) (W IA [99 maajvwco Ala IrﬂerC)? MEL/('7 ...
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