Stat 3411 Spring 2011 Assignment 6 Answers

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1 Stat 3411 Sprig 2011 Aigmet 6 Awer (A) Awer are give i 10 3 cycle (a) to Sice 150 i i the 90% 2-ided cofidece iterval, we do ot reject H 0 : µ 150 v i favor of the 2-ided alterative H a : µ 150 at the α0.10 level. (b) Two-ided Cofidece Iterval 10 df 9 1-α Cofidece 0.95 Tabled t t* Two-ided Lower Limit Two Sided Upper Limit (c) 10 Mea St Deviatio St Error Oe-ided Cofidece Iterval Tabled t t* Oe-ided Lower Limit (d) Sice 150 i i the 95% 1-ided cofidece iterval, we do ot reject H 0 : µ 150 v i favor of the 1-ided alterative H a : µ > 150 at the α0.05 level. To rule i favor of H a : µ > 150, we would eed the iterval completely above 180. (e) Oe-ided Cofidece Iterval Tabled t t* Oe-ided Upper Limit (f) Sice the upper boud i le tha 200, we reject H 0 : µ 200 i favor of H a : µ < 200. We reject H 0 : µ 200 i favor of H a : µ < 200 becaue the oe-ided iterval completely below 200. (B) (a) (i) df 9 (ii) Reject H 0 : µ 150 if t (iii) Calculated (iv) Sice t < 1.833, do ot reject H 0 : µ 150 i favor of H a : µ 150 (v) The awer are coitet, a they hould be. (b) (i) Reject H 0 : µ 150 i favor of H a : µ > 150 if t (ii) Calculated (iii) Sice t < 1.833, do ot reject H 0 : µ 150 i favor of H a : µ > 150

2 (iv) The awer are coitet, a they hould be. (c) (i) Reject H 0 : µ 200 i favor of H a : µ < 200 if t (ii) Calculated (iii) Sice t < , reject H 0 : µ 150 i favor of H a : µ > 150 (iv) The awer are coitet, a they hould be. Sectio 6.1 (3) For a 90% plu or miu, we eed 5% o both ed outide the 90% plu or miu. Ue Q(0.95) Z Thi i at the bottom of the t-table. σ 90% chace i withi ± ± σ ± of µ The tadard deviatio of 98.2 from exercie 2 i our "what if" value of σ. We eed ± ± 20. Solve for Roud up to 65. Sectio 6.3 (2) (a) Aumptio 15 idepedet meauremet o To check thi, we eed to kow how the experimet wa doe. o For example ot 5 machie with 3 bolt from each machie. Tighte of bolt o the ame machie may be correlated, ot idepedet. Normal populatio of torque required o To check thi, look at the ormal plot. o The ormal plot i reaoably traight. Normal Quatile Torque to Looe Bolt Torque

3 (b) (i) I thi book, H 0 : alway ha a ig. H 0 : µ 100. The problem ay to ee if the mea differ from 100. The mea torque could differ from 100 i either directio: H a : µ 100 (ii) i too far from 100 i either directio. 100 t i too far from 0 i either directio. t i too big. df 14, α0.05 ule tated otherwie t (iii) Top Piece Bolt Mea 111 AVERAGE(B2:B16) St Dev STDEV(B2:B16) (iv) Sice 4.40 > 2.145, reject H 0 : µ 100 i favor of H a : µ 100 (v) We have tatitically igificat evidece that the mea torque required i ot 100.

4 (c) Mea St Deviatio St Error Two-ided Cofidece Iterval 14 df 13 1-α Cofidece 0.98 Tabled t t* 6.55 Two-ided Lower Limit Two Sided Upper Limit Chapter Exercie 1 (a) Stregth 10 8,577 9,471 9,011 7,583 8,572 10,688 9,614 9,614 8,527 9,165 Mea St Deviatio St Error Two-ided Cofidece Iterval 10 df 9 1-α Cofidece 0.95 Tabled t t* Two-ided Lower Limit Two Sided Upper Limit Oe-ided Cofidece Iterval Tabled t t* Oe-ided Upper Limit Oe-ided Lower Limit

5 (e) (i) H 0 : µ 9500 v H a : µ < 9500 (ii) i too far below t i too far below 0 t i too mall, egative. df 9, α0.05 ule tated otherwie t Mea St Deviatio St Error t-tet Ho: µ 9500 Calculated t (iv) Sice > , do ot reject H 0 : µ 9500 i favor of H a : µ < 9500 at the α0.05 level. (v) We do ot have tatitically igificat evidece that the mea tregth i below Note: We have ot prove that the mea tregth i at leat Form the lower boud, with 95% cofidece the tregth could be a low a Give the cofidece iterval reult, we did't really eed to do the t-tet to fid thi out. (9) (a) 50 Mea St Deviatio St Error Two-ided Cofidece Iterval df 40 1-α Cofidece 0.95 Tabled t Uig 40 df t* Two-ided Lower Limit Two Sided Upper Limit

6 (b) Oe-ided Cofidece Iterval Tabled t t* Oe-ided Lower Limit Uig 40 df (c) (i) I thi book, H 0 : alway ha a ig. H 0 : µ The problem ay to ee if the mea exceed H a : µ > (ii) i too above t i too far above 0. t i too big. df 49. Cloet to df40 i t-table. α0.05 ule tated otherwie t (iii) (iv) Sice 2.20 > 1.684, reject H 0 : µ i favor of H a : µ > (v) We have tatitically igificat evidece that the mea wobble i greater tha (C) (a) H a : µ 180, α 0.05, 12 Reject H 0 whe t > (b) H a : µ > 180, α 0.05, 12 Reject H 0 whe t > (c) H a : µ < 180, α 0.05, 12 Reject H 0 whe t <