Question

To properly treat patients, drugs prescribed by physicians must have a potency that is accurately defined. Consequently, not only must the distribution of potency values for shipments of a drug have a mean value as specified on the drug's container, but also the variation in potency must be small. Otherwise, pharmacists would be distributing drug prescriptions that could be harmfully potent or have a low potency and be ineffective. A drug manufacturer claims that its drug is marketed with a potency of 5 + 0.1 milligram per cubic centimetre (mg/cc). A random sample of four containers gave potency readings equal to 4.95, 5.08, 5.02, and 4.91 mg/cc. (a) Do the data present sufficient evidence to indicate that the mean potency differs from 5 mg/cc? (Use a = 0.05. Round your answers to three decimal places.) 1-2. Null and alternative hypotheses: O Ho: u = 5 versus Ha: u <5 O O Ho: u = 5 versus Hau > 5 O O Hou 5 versus Ha: u = 5 11H O Ho: u = 5 versus Ha: u = 5 O Ho: u < 5 versus Ha: u > 5 3. Test statistic: t = 4. Rejection region: If the test is one-tailed, enter NONE for the unused region. 5. Conclusion: O Ho is not rejected. There is sufficient evidence to indicate that the mean potency differs from 5 mg/cc. O Ho is not rejected. There is insufficient evidence to indicate that the mean potency differs from 5 mg/cc. O Ho is rejected. There is insufficient evidence to indicate that the mean potency differs from 5 mg/cc.

Answer 1

Gova that Acoreday to uebens manufarture claimo that its olaug keh with petney 510l millgrams fen cubie cortimedea. A9nandomsample ofeen eentainens eve psteney 91 eaelngs egal t 495,5.08, 5.0 ael 4y mgfae. a) indds The data pnesent sufficiant evidlance te unlicak that mean Telency dffems frem Smg/u [xoes) the alew Do t lata pnessod suffeient evidenee te imodient that thmean potency offfons foom smg/e M=S we have obseavat.ons ane n« [445, 5.08,502 an) 49,) )The ull hy pothes:'s ) The Altenatwe bypethesis ) andh& s is H: M-s vlen sus * To fn test statistic

ample mean Sample stanclad oleviatian Sampla Sie pepalahion mean lews 4.95t S.08 + 5-02 +491 १.१६ ие nouw do find s - %) 52. L495-491)508-49, E02-49), (ees)" (-c o) e00)o .00566 O-00'566 0.075234 4 49 -5

-D.0lxu O-07523 -0 02 o 07522 0.269 faiteneject Hence hene we Pejeetion ion Now the test is enetaili t lf feo-faila tt, df Conclusion: Ho is n nejeceted Thene is insu/ficiend eviclevce fe indicot fhat the mean p0(aney olifters fnom Smglee

Thpotancy Values will fall into the intonval so toime = 0-05 q002 Thlhypethesis . ooa Te Altnatve hy pottesis. " test statistc = »2 s 566 (4-1) 0 0s66 3(00544) Gv)Pejection negicn is one faile The test Conelusion is nt nejteS. Thene is in sufticient eviclence to inaliate ptancy fens fmom the specifiel non limit that the aniation in