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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.
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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. ..
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- Summer '04
- JOHNSON
- Statistics, Probability