Homework 7 with Solutions - Introduction to Statistics | STAT 1222, Assignments of Statistics

Download Homework 7 with Solutions - Introduction to Statistics | STAT 1222 and more Assignments Statistics in PDF only on Docsity! Homework 7 Stat 1222-010 (Professor: Dr. Biswas) Due: Tue 3/31/09 Name: ID#: i. An auto maker claims that the mean gas mileage of its luxury sedan is at least 25 miles per gallon. A tandom sample of forty such cars had a mean of 23 miles per gallon and a standard deviation of 5 miles per gallon. Test the auto maker’s claim. Ade wear fe mM ileage {a) (2 pts) State the null and the alternative hypotheses. Identify the claim. State whether the test is right. sided, left sided or two sided. Ho: nes ter dry —» Lft-tniled. CEL niea\ {b) (4 pts) Find the critical values at level a = .08 and state the rejection rule. State your decision. ZR 5 23-25 _ pie ned Bia is 7 ey [le Sectim vwle- Refect He if B <-1-41, Decision Reject Hy - (c) (4 pts) Find the P-value. Based on the P-value, what is your decision at level « = .04. Why? ‘Pe Aten in lft tail = bs 75 Vt +005 F. Bs72£3 Rejection Mube> Ideject Ue if PSkz-0y. 19 0b Seed! Feo bL wghek, $0 Vecwwim Teg eef k. 2. A certain restaurant claims that its hamburgers have a fat content of 10 grams. A health inspector wants to test this claim and finds that a random sample of 50 hamburgers Ras & mean of 10,5 grams sew Zid a standard deviation of 2.5 grams, Showing your steps as in the previous nart,.test_tbe restaurant’. claim and state your decision. MAM = ay Lea ye f af tevite nt . {a) (2 pts) State the mill and the alternative hypotheses, Identify the claim. State whether the test is right sided, left sided or two sided. Claim A = lo ) Opporde: MF io (laiw Hy: Ake 10) Ha> M fl0 —> Two- tailed (b) (4 pts) Find the P-value. Based on the P-value, what is your decision at level a = .01. Why? ne 50, Kx loe5 p29. te RM. pee- jo i pees “BIE ape 4] 29Meo 4 obseved Bel Pur Zr-et4d = -\5ed. * Decisis tale: Leject Wo if PL +01 5 Pe s86 > “Oren; py r4toF= +9443 ®, Decision, Do wot Seject H, = 5 (c) (4 pts) Find the critical valnes at level a = .05 and state thé rejection rule. State your Yeon’ ote =O ‘v In the context of the problem, identify the Type I error. A Yeu ; Ady ertion Bim = [eject Ho GES 4G ow Z> [-46 “petty It TELM Dowel mged py, ” Decigien 7 Ve