Section 18: confidence interval & hypothesis testing using sample means (sigma unknown)

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1 Sectio 18: cofidece iterval & hypothei tetig uig ample mea (igma ukow) 1. A imple radom ample of 40 package of Chip Ahoy cookie reveal a average of chocolate chip per package, with a tadard deviatio of chip. (a) Fid 95%, 90%, ad 99% cofidece iterval for the mea umber of chocolate chip i all Chip Ahoy package. df % cofidece: t ± ± ( , ) 90% cofidece: t ± ± ( , ) 99% cofidece: t ± ± ( , ) (b) The compay claim that Chip Ahoy package cotai o average 1300 chocolate chip. Do we have evidece at the 10%, 5%, 1% level that they re exaggeratig? H 0 : μ 1300 H a : μ < 1300 t tail: > > p value: 0.01 < P < 0.025

2 (c) Jack claim that Chip Ahoy package cotai o average 1300 chocolate chip. Do we have evidece at the 10%, 5%, 1% level that he i mitake? H a : μ tail: > > p value: 0.02 < P < How may lick doe it take to get to the Tootie Roll ceter of a Tootie Pop? A imple radom ample of 22 attempt yield a average of 508 lick per pop, with a tadard deviatio of 164 lick. (a) Fid 95%, 90%, ad 99% cofidece iterval for the mea umber of lick for all pop. df % cofidece: t ± ± (435.27, ) 90% cofidece: t ± ± (447.83, ) 99% cofidece: t ± ± (409.01, )

3 (b) Mr. Owl claim that it take o average 500 lick. Do we have evidece at the 10%, 5%, 1% level that he uderetimatig? Do we have evidece at the 10%, 5%, 1% level that he mitake? H 0 : μ 500 H a : μ > 500 t tail: > p value: 0.25 < P P.10 H a : μ tail: > p value: 0.50 < P P.10 (c) Mr. Turtle claim that it take o average 580 lick. Do we have evidece at the 10%, 5%, 1% level that he overetimatig? Do we have evidece at the 10%, 5%, 1% level that he mitake? H 0 : μ 580 H a : μ < 580 t

4 1 tail: > > p value: < P < 0.05 H a : μ tail: > > p value: 0.05 < P < What i the average commute time for people goig to work i the ortheat? A imple radom ample of 30 people who drive to work i the ortheat reult i a mea time of miute with a tadard deviatio of miute. (a) Fid 80%, 98%, ad 95% cofidece iterval for the average commute time i the ortheat. df % cofidece: t ± ± (25.57,30.37) 98% cofidece: t ± ± (23.46, 32.48) 95% cofidece: t ± ±

5 (24.22, 31.72) (b) Jack claim that o average i take 32 miute for omeoe i the ortheat to get to work. Do we have evidece at the 10%, 5%, 1% level that he overetimatig? Do we have evidece at the 10%, 5%, 1% level that he mitake? H 0 : μ 32 H a : μ < 32 t tail: > > p value: 0.01 < P < H a : μ 32 2 tail: > > p value: 0.02 < P < 0.05 (c) Sam claim that o average i take 25 miute for omeoe i the ortheat to get to work. Do we have evidece at the 10%, 5%, 1% level that he uderetimatig? Do we have evidece at the 10%, 5%, 1% level that he mitake? H 0 : μ 25 H a : μ > 25

6 t tail: > > p value: 0.05 < P < H a : μ 25 2 tail: > > p value: 0.10 < P < 0.15 P Joatha Ket ha bee uig a certai brad of chicke feed for year, ad o average hi chicke weigh 62.2 ouce. He tet a ew type of chicke feed o 9 chicke, ad their average weight i ouce, with a tadard deviatio of ouce. (a) Fid 99%, 95%, ad 85% cofidece iterval for the average weight that would be gaied by all chicke uig the ew feed. df % cofidece: t ± ± (62.07, 66.69) 95% cofidece: t ± ± (62.79, 65.97)

7 85% cofidece: t ± ± (63.28, 65.48) (b) Doe Joatha have evidece at the 10%, 5%, 1% level that the ew chicke feed i better tha the old brad? H 0 : μ 62.2 H a : μ > 62.2 t tail: > > p value: < P < 0.01 P < A certai comedia meaure the effectivee of hi routie by the umber of time he ha to wait for laughter to ubide before cotiuig; hi old routie averaged 63.2 time. He i tryig a ew routie, ad of it 15 performace, the average umber of time he had to wait wa time, with a tadard deviatio of 19.3 time. (a) Fid 99%, 95%, 90% cofidece iterval for the average umber of waitig time for all poible performace of hi ew routie (i.e., hi meaure of how good it i). df % cofidece: t ± ± (54.69, 84.37) 95% cofidece: t 2.145

8 ± ± (58.84, 80.22) 90% cofidece: t ± ± (60.75, 78.31) (b) Doe he have evidece at the 10%, 5%, 1% level that hi ew routie i better? H 0 : μ 63.2 H a : μ > 63.2 t tail: > > p value: 0.10 < P < P A imple radom ample of 33 brow M&M reveal that their average weight i gram with a tadard deviatio of gram. (a) Fid 80%, 90%, 95%, 99% cofidece iterval for the true average weight of (all) brow M&M. df % cofidece: t ± ± (0.9038, ) 90% cofidece: t 1.694

9 ± ± (0.9012, ) 95% cofidece: t ± ± (0.8988, ) 99% cofidece: t ± ± (0.8940, ) (b) Horatio, a lover of brow M&M with too much time o hi had, grumble that he believe that o average, a brow M&M weigh oly gram. Do we have evidece that Horatio i uderetimatig the average weight of brow M&M? H 0 : μ H a : μ > t tail: > p value: 0.25 < P P A imple radom ample of 20 tatitic tudet durig a tatitic exam give a average pule rate 74.4 with a tadard deviatio of 10. (a) Fid 90%, 95%, 99% cofidece iterval for the average pule rate of all tatitic tudet durig a exam.

10 df % cofidece: t ± ± (70.53, 78.27) 95% cofidece: t ± ± (69.72, 79.08) 99% cofidece: t ± ± (68.00, 80.80) (b) If a good exercie regime would give uch tudet a pule rate of 60, do we have evidece at the 10%, 5%, 1% level that a tatitic exam ha a greater effect o pule rate tha uch exercie? H 0 : μ 60 H a : μ > 60 t tail: > p value: P < P <.01

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