Stat 3411 Sprig 2011 Aigmet 6 Awer (A) Awer are give i 10 3 cycle (a) 149.1 to 187.5 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 2.262 t* 23.71 Two-ided Lower Limit 144.59 Two Sided Upper Limit 192.01 (c) 10 Mea 168.30 St Deviatio 33.15 St Error 10.48 Oe-ided Cofidece Iterval Tabled t 1.833 t* 19.22 Oe-ided Lower Limit 149.08 (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 1.833 t* 19.22 Oe-ided Upper Limit 187.5 (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 1.833. (iii) Calculated 1.746 (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 1.833. (ii) Calculated 1.746 (iii) Sice t < 1.833, do ot reject H 0 : µ 150 i favor of H a : µ > 150
(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 -1.833. (ii) Calculated -3.024 (iii) Sice t < -1.833, 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 0.05 1.645. Thi i at the bottom of the t-table. σ 90% chace i withi ± 1.645 ± 1.645 σ ± 1. 645 of µ The tadard deviatio of 98.2 from exercie 2 i our "what if" value of σ. We eed ± 1.645 98.2 ± 20. Solve for 65.24. 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 2.50 2.00 1.50 1.00 0.50 0.00-0.50-1.00 90 100 110 120 130 Torque -1.50-2.00-2.50
(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 2.145 (iii) Top Piece Bolt 1 110 2 115 3 105 4 115 5 115 6 120 7 110 8 125 9 105 10 130 11 95 12 110 13 110 14 95 15 105 Mea 111 AVERAGE(B2:B16) St Dev 9.6732 STDEV(B2:B16) 100 9.67 15 2.50 111 100 2.498 4.40 (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.
(c) Mea 111.00 St Deviatio 9.673 St Error 2.498 Two-ided Cofidece Iterval 14 df 13 1-α Cofidece 0.98 Tabled t 2.624 t* 6.55 Two-ided Lower Limit 104.45 Two Sided Upper Limit 117.55 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 9082.20 St Deviatio 841.87 St Error 266.22 Two-ided Cofidece Iterval 10 df 9 1-α Cofidece 0.95 Tabled t 2.262 t* 602.2 Two-ided Lower Limit 8480.0 Two Sided Upper Limit 9684.4 Oe-ided Cofidece Iterval Tabled t 1.833 t* 488.0 Oe-ided Upper Limit 9570.2 Oe-ided Lower Limit 8594.2
(e) (i) H 0 : µ 9500 v H a : µ < 9500 (ii) i too far below 9500 9500 t i too far below 0 t i too mall, egative. df 9, α0.05 ule tated otherwie t -1.833 Mea 9082.20 St Deviatio 841.87 St Error 266.22 t-tet Ho: µ 9500 Calculated t -1.569 (iv) Sice -1.57 > -1.833, 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 9500. Note: We have ot prove that the mea tregth i at leat 9500. Form the lower boud, with 95% cofidece the tregth could be a low a 8594. Give the cofidece iterval reult, we did't really eed to do the t-tet to fid thi out. (9) (a) 50 Mea 0.0287 St Deviatio 0.0119 St Error 0.00168 Two-ided Cofidece Iterval df 40 1-α Cofidece 0.95 Tabled t 2.021 Uig 40 df t* 0.0034 Two-ided Lower Limit 0.0253 Two Sided Upper Limit 0.0321
(b) Oe-ided Cofidece Iterval Tabled t 1.684 t* 0.0028 Oe-ided Lower Limit 0.0259 Uig 40 df (c) (i) I thi book, H 0 : alway ha a ig. H 0 : µ 0.025 The problem ay to ee if the mea exceed 0.025. H a : µ > 0.025 (ii) i too above 0.025 0.025 t i too far above 0. t i too big. df 49. Cloet to df40 i t-table. α0.05 ule tated otherwie t 1.684 (iii) 0.025 0.0119 0.00168 50 0.0287 0.025 2.20 0.00168 (iv) Sice 2.20 > 1.684, reject H 0 : µ 0.025 i favor of H a : µ > 0.025 (v) We have tatitically igificat evidece that the mea wobble i greater tha 0.025. (C) (a) H a : µ 180, α 0.05, 12 Reject H 0 whe t > 2.201 (b) H a : µ > 180, α 0.05, 12 Reject H 0 whe t > 1.796 (c) H a : µ < 180, α 0.05, 12 Reject H 0 whe t < -1.796